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Form of continuity for functions
absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity. The notion of absolute continuity allows
Absolute_continuity
Comic book series by DC Comics
Absolute Batman is an American monthly superhero comic book series published by DC Comics, featuring an alternate version of the character Batman. The
Absolute_Batman
Mathematical concept
In mathematics, uniform integrability is an important concept in real analysis, functional analysis and measure theory, and plays a vital role in the theory
Uniform_integrability
DC Comics imprint
Absolute Wonder Woman and Absolute Superman. The Absolute Universe (AU) is an all-new continuity separate from the DC Universe (DCU) overseen by Scott
Absolute_Universe
Continuous function that is not absolutely continuous
counterexample in analysis, because it challenges naive intuitions about continuity, derivative, and measure. Although it is continuous everywhere, and has
Cantor_function
continuity, continuous, and continuum are used in a variety of related ways. Continuous function Absolutely continuous function Absolute continuity of
List of continuity-related mathematical topics
List_of_continuity-related_mathematical_topics
Mathematical function with no sudden changes
everywhere. Continuity (mathematics) Absolute continuity Approximate continuity Dini continuity Equicontinuity Geometric continuity Parametric continuity Classification
Continuous_function
Strong form of uniform continuity
mathematical analysis, Lipschitz continuity, named after German mathematician Rudolf Lipschitz, is a strong form of uniform continuity for functions. Intuitively
Lipschitz_continuity
Result in measure theory
In mathematics — specifically, in measure theory — Malliavin's absolute continuity lemma is a result due to the French mathematician Paul Malliavin that
Malliavin's absolute continuity lemma
Malliavin's_absolute_continuity_lemma
Approximation of a function by a polynomial
R_{k}(x)=\int _{a}^{x}{\frac {f^{(k+1)}(t)}{k!}}(x-t)^{k}\,dt.} Due to the absolute continuity of f(k) on the closed interval between a {\textstyle a} and x {\textstyle
Taylor's_theorem
same support. Thus the notion of contiguity extends the concept of absolute continuity to the sequences of measures. The concept was originally introduced
Contiguity (probability theory)
Contiguity_(probability_theory)
Generalization of the Riemann integral
were given by Nikolai Luzin (using variations on the notions of absolute continuity), and by Oskar Perron, who was interested in continuous major and
Henstock–Kurzweil_integral
Probability distribution in measure theory
are singular distributions in two dimensions. Absolute continuity (measure theory) – Form of continuity for functionsPages displaying short descriptions
Singular_measure
Prevention and recovery from threats to a company
Business continuity may be defined as "the capability of an organization to continue the delivery of products or services at pre-defined acceptable levels
Business_continuity_planning
Theorem in mathematics and economics
strong assumptions, in many applications weaker conditions such as absolute continuity, differentiability almost everywhere, or left- and right-differentiability
Envelope_theorem
Initial result in using test functions to find extremum
almost everywhere (thus, in all continuity points), and differentiability of g is interpreted as local absolute continuity (rather than continuous differentiability)
Fundamental lemma of the calculus of variations
Fundamental_lemma_of_the_calculus_of_variations
{\displaystyle \lim _{n\to \infty }\lambda _{n}(B)=\lambda (B)} . Then the absolute continuity of the λ n {\displaystyle \lambda _{n}} with respect to m {\displaystyle
Vitali–Hahn–Saks_theorem
Soviet and Russian mathematician (born 1934)
Mathematicians (ICM) in Nice. In 1978 he was a Plenary Speaker with talk Absolute Continuity and Singularity of Probability Measures in Functional Spaces at the
Albert_Shiryaev
Definition of mathematical integration
than absolute continuity but is satisfied by any approximately differentiable function. This is the concept of generalized absolute continuity; generalized
Khinchin_integral
Study of rates of change
the relation between derivation and integration with the notion of absolute continuity. Later the theory of distributions (after Laurent Schwartz) extended
Differential_calculus
Mathematical theorem
atomless, then the uniform integrability is equivalent to the uniform absolute continuity of integrals. Let ( X , A , μ ) {\displaystyle (X,{\mathcal {A}}
Vitali_convergence_theorem
Type of function
singular functions to be used in partial differential equations, etc. Absolute continuity Mathematical singularity Generalized function Distribution Minkowski's
Singular_function
Catholic lay religious order
passive legation for the Order, which is legally important for the absolute continuity of international status, regardless of the former territorial possession
Sovereign Military Order of Malta
Sovereign_Military_Order_of_Malta
Operator in analysis and probability theory
5802/afst.962. hdl:20.500.11850/146400. Kunita, Hiroshi (1969). "Absolute continuity of Markov processes and generators". Nagoya Mathematical Journal
Carré_du_champ_operator
Mathematical statistics distance measure
{\displaystyle Q(x)=0} implies P ( x ) = 0 {\displaystyle P(x)=0} (absolute continuity). Otherwise, it is often defined as + ∞ {\displaystyle +\infty }
Kullback–Leibler_divergence
Theorem
is chosen to be trace. Belavkin introduced the notion of complete absolute continuity of one completely positive map with respect to another (reference)
Stinespring_dilation_theorem
French mathematician (1925–2010)
Alma mater University of Paris Known for Malliavin derivative Malliavin's absolute continuity lemma Malliavin calculus Probabilistic proof of Hörmander's theorem
Paul_Malliavin
Russian mathematician (born 1961)
proved (with Michael Röckner) the famous Shigekawa conjecture on the absolute continuity of invariant measures of diffusion processes. In 1999, in a joint
Vladimir_Bogachev
Relation among continuous functions
functions of random variables, and their convergence. Absolute continuity – Form of continuity for functions Classification of discontinuities – Mathematical
Equicontinuity
the same, the treaties remained valid, and the powers recognized absolute continuity. Thus, for International Law, a new State was not born; what occurred
List of modern sovereign states by date of formation
List_of_modern_sovereign_states_by_date_of_formation
Uniform restraint of the change in functions
{\displaystyle f} . The difference between uniform continuity and (ordinary) continuity is that in uniform continuity there is a globally applicable δ {\displaystyle
Uniform_continuity
Type of Borel measure
^{n}\ll \lambda ^{n}} , where ≪ {\displaystyle \ll } stands for absolute continuity of measures; is supported on all of Euclidean space: supp ( γ n
Gaussian_measure
Definition of mathematical integration
zero on a negligible set. Pfeffer defined a notion of generalized absolute continuity A C G ∗ {\displaystyle ACG^{*}} , close to but not equal to the definition
Pfeffer_integral
Type of measure in measure theory
is strictly positive, μ ( U ) > 0 ; {\displaystyle \mu (U)>0;} by absolute continuity, ν ( U ) > 0 {\displaystyle \nu (U)>0} as well. Hence, strict positivity
Strictly_positive_measure
Fatou's lemma Frostman's lemma (geometric measure theory) Malliavin's absolute continuity lemma Lindelöf's lemma Urysohn's lemma Tube lemma Morse lemma
List_of_lemmas
Expressing a measure as an integral of another
{\displaystyle \nu } on Σ {\displaystyle \Sigma } , without assuming any absolute continuity. Then there exist unique signed measures ν a {\displaystyle \nu _{a}}
Radon–Nikodym_theorem
Statement on solutions to ordinary differential equations
equation almost everywhere and y satisfies the initial condition. The absolute continuity of y implies that its derivative exists almost everywhere. Consider
Carathéodory's existence theorem
Carathéodory's_existence_theorem
of a function Uniform continuity Modulus of continuity Lipschitz continuity Semi-continuity Equicontinuous Absolute continuity Hölder condition – condition
List_of_real_analysis_topics
Physical quantity of hot and cold
one of the seven base units in the International System of Units (SI). Absolute zero, i.e., zero kelvin, 0 K = −273.15 °C, or -459.67 °F, is the lowest
Temperature
American mathematician
PMID 16588415. Calkin, J. W. (1940). "Functions of several variables and absolute continuity, I". Duke Mathematical Journal. 6: 170–186. doi:10.1215/S0012-7094-40-00614-7
John_Williams_Calkin
Statistical formula
example, which impose diffeomorphism constraints in order to enforce absolute continuity of Q θ {\displaystyle Q_{\theta }} and P {\displaystyle P} . Stein
Stein_discrepancy
Russian-Israeli mathematician (1936–2019)
Google Books Kabanov, Yu. M., Liptser, R. Sh. and Shiryaev, A. N. "Absolute continuity and singularity of locally absolutely continuous probability distributions
Robert_Liptser
Function from sets to numbers
{\displaystyle \mu ^{*}} to this family is a measure. Absolute continuity (measure theory) – Form of continuity for functionsPages displaying short descriptions
Set_function
Property of functions which is weaker than continuity
analysis, semicontinuity (or semi-continuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function
Semi-continuity
German mathematical physicist (born 1945)
PMID 14995799. Hupfer, T.; Leschke, H.; Müller, P.; Warzel, S. (2001). "The Absolute Continuity of the Integrated Density of States for Magnetic Schrödinger Operators
Hajo_Leschke
SI unit of temperature
Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By definition
Kelvin
Length in a vector space
following properties, where | s | {\displaystyle |s|} denotes the usual absolute value of a scalar s {\displaystyle s} : Subadditivity / Triangle inequality:
Norm_(mathematics)
Inequality in information theory
the above, the notation P ≪ Q {\displaystyle P\ll Q} stands for absolute continuity of P {\displaystyle P} with respect to Q {\displaystyle Q} , and
Bretagnolle–Huber_inequality
Statistical method
In statistics, Yates's correction for continuity (or Yates's chi-squared test) is a statistical test commonly used when analyzing count data organized
Yates's correction for continuity
Yates's_correction_for_continuity
Celtic chariot tomb
Cà'Morta area of influence. However, this phenomenon is not marked by absolute continuity over time. Several waves of Celtic tribes migrated between the 15th
Ca'_Morta_tomb
Supreme authority within a territory
An important factor of sovereignty is its degree of absoluteness. A sovereign power has absolute sovereignty when it is not restricted by a constitution
Sovereignty
Superhero media franchise
continuity and story across live-action films and television, animation, and video games. Concurrent DC adaptations that do not fit this continuity are
DC_Universe_(franchise)
Dominican friar who became an anti-Trinitarian
Novi Testamentum (1572), is Palaeologus' argument supporting the absolute continuity and consistency of the Old and New Testaments. Key to this is his
Jacob_Palaeologus
space Integration by parts operator Malliavin derivative Malliavin's absolute continuity lemma Ornstein–Uhlenbeck operator Skorokhod integral Random dynamical
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
American mathematician
doi:10.5802/aif.387. ISSN 0373-0956. Walsh, Bertram (1971). "Mutual absolute continuity of sets of measures". Proceedings of the American Mathematical Society
Bertram_John_Walsh
Filipino-American comic book writer
Marvel Comics, and DC Comics. His most notable works are The Ultimates, Absolute Martian Manhunter and Assorted Crisis Events. Camp received five Eisner
Deniz_Camp
American mathematician (1927-1984)
Morrey, Charles B. Jr. (1940), "Functions of several variables and absolute continuity, II", Duke Mathematical Journal, 6 (1): 187–215, doi:10.1215/S0012-7094-40-00615-9
Charles_B._Morrey_Jr.
Israeli scientist (born 1926–2015)
Süleyman; Zakai, Moshe (1993). "Applications of the degree theorem to absolute continuity on Wiener space". Probability Theory and Related Fields. 95 (4):
Moshe_Zakai
convergence theorem Fatou's lemma Absolutely continuous Uniform absolute continuity Total variation Radon–Nikodym theorem Fubini's theorem Double integral
List of integration and measure theory topics
List_of_integration_and_measure_theory_topics
1987 story arc in Batman comic book series
alliance against Gotham's criminal underworld. In an effort to resolve continuity errors in the DC Universe, Marv Wolfman and George Pérez produced the
Batman:_Year_One
list of the Animorphs books by K. A. Applegate, as applies to storyline continuity. The Andalite Chronicles (c. 1976, 1980s, 1997) This book is divided into
List_of_Animorphs_books
of random fields. For example, he established conditions for the absolute continuity and singularity of measures that correspond to Gaussian random fields
Myhailo_Yadrenko
English disc jockey
afternoon show. She is also a continuity announcer for Sky One and Sky Movies. In 2015 Claire Sturgess joined Absolute Radio, taking the 4-6 pm slots
Claire_Sturgess
Canadian mathematician
ISBN 978-1-4614-5391-8. Hare, Kathryn E.; He, Jimmy. (2017), "The absolute continuity of convolution products of orbital measures in exceptional symmetric
Kathryn_E._Hare
1958 book by Raya Dunayevskaya
direct encounter with Hegel's dialectical philosophy and particularly his Absolutes, which she interpreted as posing a dual movement from practice to theory
Marxism_and_Freedom
Function defined by multiple sub-functions
the following conditions have to fulfilled in addition to those for continuity above: its sub-functions are differentiable on the corresponding open
Piecewise_function
Single-winner electoral system
majority would also oppose giving a lower grade. This rule means that the absolute majority of the electors judge that a candidates merits at least its median
Graduated_majority_judgment
Concept in religion, ethics, and philosophy
capable", and their absolute sense emerges only around 400 BC, with Pre-Socratic philosophy, in particular Democritus. Morality in this absolute sense solidifies
Good
New Zealand-American mathematician
334–353. doi:10.1016/0022-1236(70)90013-3. Shale, David (1973). "Absolute continuity of Wiener processes". Journal of Functional Analysis. 12 (3): 321–334
David_Shale
Form of government ruled by a monarch, or a polity with this form of government
There are conventionally two types of monarchy: absolute monarchy and constitutional monarchy. Absolute monarchies, of which there are approximately twelve
Monarchy
Limited comic book series by Jeph Loeb (1996–1997)
Two-Face, incorporating elements of the story in Batman: Annual #14. In continuity terms, The Long Halloween continues the story of "Batman: Year One" for
Batman:_The_Long_Halloween
Statistical hypothesis test
suggested a correction for continuity that adjusts the formula for Pearson's chi-squared test by subtracting 0.5 from the absolute difference between each
Chi-squared_test
British entertainer and presenter (born 1976)
had other CBBC hits including The Legend of Dick and Dom, Diddy TV and Absolute Genius with Dick and Dom. From 2007 to 2008 McCourt and Wood hosted the
Richard_McCourt
Comic book series (published 2006)
v t e Batman publications and storylines Current series Absolute Batman Absolute Catwoman Batgirl Batman Batman/Superman: World's Finest Birds of Prey
Batman_and_the_Monster_Men
DC Comics superhero
comics continuity and in The New 52 continuity, Wonder Woman was one of the many major books to be relaunched for the start of the new continuity, with
Wonder_Woman
Comic book series
Comics / WildStorm imprint, introduced Promethea into its mainstream continuity by way of the comic Justice League of America #24. The controversial storyline
Promethea
American comic book series
embodied by its many continuity reboots. The new Drummer reveals herself to be Jakita Wagner, the sole survivor of the Planetary continuity becoming erased
Planetary_(comics)
Method for finding limits in calculus
(video, Khan Academy) Stewart, James (2008). "Chapter 15.2 Limits and Continuity". Multivariable Calculus (6th ed.). pp. 909–910. ISBN 978-0495011637.
Squeeze_theorem
Discussion about changing the Japanese throne's laws of succession
history of the Imperial Family and in light of considerations such as the continuity of public activities, the Imperial House Law should be amended and work
Japanese imperial succession debate
Japanese_imperial_succession_debate
2026 Marvel Studios television special
Special Presentation in the Marvel Cinematic Universe (MCU), sharing continuity with the films and television series of the franchise. Produced by Marvel
The_Punisher:_One_Last_Kill
American superhero comic book
Absolute Catwoman is an American superhero comic book miniseries published by DC Comics, focusing on the anti-heroine Catwoman. The series, written by
Absolute_Catwoman
DC's continuity. In chronological order (with issue and date of first appearance) In 2024, DC Comics created the Absolute Universe, including Absolute Wonder
List_of_Wonder_Woman_enemies
List of alternate universes set in the DC Comics media
The DC Multiverse is a fictional continuity construct used in numerous DC Comics publications. The Multiverse has undergone numerous changes since its
List_of_DC_Multiverse_worlds
Figure of speech of implicit comparison
and innumerable characteristics; they avoid discretizing the perceived continuity of experience and are thus closer to experience and consequently more
Metaphor
Collection of character sketches
can write verses, not a poem. There is no principle of massing or of continuity in his productions—neither height nor breadth nor depth of capacity. There
The_Spirit_of_the_Age
1993 spy novel by John le Carré
Tailor of Panama (1996) Single & Single (1999) The Constant Gardener (2001) Absolute Friends (2003) The Mission Song (2006) A Most Wanted Man (2008) Our Kind
The_Night_Manager
American lawyer
Studies 317 (2004) (with Susan Athey & Kyle Bagwell) The Role of Absolute Continuity in Merging of Opinions and Rational Learning, 29 1/2 Games and Economic
Chris_William_Sanchirico
Mathematical property of algebraic structures
absolute value functions. By Ostrowski's theorem, every non-trivial absolute value on the rational numbers is equivalent to either the usual absolute
Archimedean_property
Upcoming Indian Malayalam-language film
First Mid-credits Scene: The sequence addresses the immediate narrative continuity of Marco. It unravels the underlying mystery behind the kidnapping of
Kattalan
Bias towards continuity
habit, law, generality, continuity, "all". Peirce held that firstness and secondness, as elements, give thirdness and continuity something upon which to
Synechism
1936 military plot
telegraph offices, prisons, power plants, banks, hydrological installations; continuity of their operations was to be ensured. Finally, 4) all would-be focos
Spanish military conspiracy of 1936
Spanish_military_conspiracy_of_1936
Function returning minus 1, zero or plus 1
are confirmed by any of the various equivalent formal definitions of continuity in mathematical analysis. A function f ( x ) {\displaystyle f(x)} , such
Sign_function
then-entire series roster is playable. In the 2011 reboot that retells the continuity of the first three games, she is immediately playable and plays a minor
Characters of the Mortal Kombat series
Characters_of_the_Mortal_Kombat_series
Comic book limited series by Darwyn Cooke
series was collected into two trade paperback volumes in 2004 and 2005, an Absolute Edition in 2006 and a deluxe edition in 2015. The story was adapted into
DC:_The_New_Frontier
Form of government
is not alone in making decisions. Constitutional monarchies differ from absolute monarchies (in which a monarch is the only decision-maker) in that they
Constitutional_monarchy
Mathematical problem in classical harmonic analysis
requires the comprehension of pointwise convergence, uniform convergence, absolute convergence, Lp spaces, summability methods and the Cesàro mean. Consider
Convergence_of_Fourier_series
Science fantasy young adult book series
into the series' continuity (the Animorphs Chronicles and Megamorphs books) and two that are gamebooks not fitting into the continuity (the Alternamorphs
Animorphs
Instantaneous rate of change (mathematics)
{f(a+h)-f(a)}{h}}\right|<\varepsilon ,} where the vertical bars denote the absolute value. This is an example of the (ε, δ)-definition of limit. If the function
Derivative
from January 2018. (vol. 3) #1–5 (November 2019 – December 2020). Out of continuity miniseries. (vol. 4) #1–11 (December 2022 – October 2023) Spider-Man Unlimited
List_of_Spider-Man_titles
Ancestor of the Uralic languages
sentences (if the language is inflectional), is re-analyzed as an unmarked absolutive, and the marked agent as ergative. Proto-Uralic was an SOV language with
Proto-Uralic_language
ABSOLUTE CONTINUITY
ABSOLUTE CONTINUITY
Girl/Female
Indian, Sanskrit
Alone; One; Absolute
Boy/Male
Tamil
Keval Kumar | கேவலகà¯à®®à®¾à®°
Absolute
Keval Kumar | கேவலகà¯à®®à®¾à®°
Boy/Male
Indian
Absolute.
Boy/Male
Gujarati, Hindu, Indian, Malayalam, Marathi, Sanskrit
Absolute Brahma
Boy/Male
Indian, Sanskrit
Absolute; Aloneness
Boy/Male
Hindu
The supreme absolute truth
Boy/Male
Tamil
Kevalin | கேவாலீந
Seeker of the absolute
Kevalin | கேவாலீந
Boy/Male
Hindu
Resolute
Boy/Male
Tamil
Parabrahmana | பரபà¯à®°à®¹à¯à®®à®¨à®¾
The supreme absolute truth
Parabrahmana | பரபà¯à®°à®¹à¯à®®à®¨à®¾
Boy/Male
Indian, Sanskrit
Alone; One; Absolute
Boy/Male
Tamil
Chidaakaash | சிதாகாஷ
Absolute Brahma
Chidaakaash | சிதாகாஷ
Boy/Male
Indian, Sanskrit
Seeker of the Absolute
Girl/Female
Gujarati, Hindu, Indian, Kannada, Sanskrit
Absolute; Aloneness
Boy/Male
Indian, Sanskrit
Alone; One; Absolute
Boy/Male
Hindu, Indian, Kannada, Marathi, Telugu, Traditional
Absolute Brahma
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Telugu
Absolute
Boy/Male
Hindu
Absolute
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Telugu
Absolute
Boy/Male
Tamil
Chidakash | சிதாகாஷ
Absolute Brahma
Chidakash | சிதாகாஷ
Boy/Male
Arabic, Muslim
Absolute; Unlimited
ABSOLUTE CONTINUITY
ABSOLUTE CONTINUITY
Boy/Male
Hindu, Indian
Lord Murugan
Girl/Female
Hindu, Indian, Kannada, Marathi
Summer Season
Girl/Female
Biblical
Rupture, fracture.
Girl/Female
Biblical
House of expulsion.
Surname or Lastname
English (mainly Devon and Cornwall)
English (mainly Devon and Cornwall) : nickname from Norman French buge ‘mouth’ (Late Latin bucca), applied either to someone with a large or misshapen mouth or to someone who made excessive use of his mouth, i.e. a garrulous, indiscreet, or gluttonous person. The word is also recorded in Middle English in the sense ‘victuals supplied for retainers on a military campaign’, and the surname may therefore also have arisen as a metonymic occupational name for a medieval quartermaster.Scottish (Caithness and Orkney) : unexplained.
Male
French
Old French form of Latin Eustachius, EUSTACHE means "fruitful."
Boy/Male
Tamil
Snehardh | ஸà¯à®¨à¯‡à®¹à®¾à®°à¯à®¤
A true friend
Girl/Female
Arabic, Muslim
Pinch (of Snuff)
Girl/Female
Arabic, Muslim
Opening
Boy/Male
Arabic, Hebrew, Muslim
Intelligent; A Prophet Name
ABSOLUTE CONTINUITY
ABSOLUTE CONTINUITY
ABSOLUTE CONTINUITY
ABSOLUTE CONTINUITY
ABSOLUTE CONTINUITY
n.
Doctrine of absolute decrees.
a.
Complete in itself; perfect; consummate; faultless; as, absolute perfection; absolute beauty.
a.
Loose; free; liberal; as, a solute interpretation.
n.
Absolute municipal self-government.
v. t.
To set free, or release, as from some obligation, debt, or responsibility, or from the consequences of guilt or such ties as it would be sin or guilt to violate; to pronounce free; as, to absolve a subject from his allegiance; to absolve an offender, which amounts to an acquittal and remission of his punishment.
a.
Loosed from any limitation or condition; uncontrolled; unrestricted; unconditional; as, absolute authority, monarchy, sovereignty, an absolute promise or command; absolute power; an absolute monarch.
n.
Absolute renunciation or repudiation.
v. t.
To absolve; as, to solute sin.
n.
One who is resolute; hence, a desperado.
a.
Unqualified; absolute; entire; sheer.
a.
Not immediately dependent on the other parts of the sentence in government; as, the case absolute. See Ablative absolute, under Ablative.
v. i.
To become obsolete; to go out of use.
adv.
In an absolute, independent, or unconditional manner; wholly; positively.
a.
Not adhering; loose; -- opposed to adnate; as, a solute stipule.
a.
No longer in use; gone into disuse; disused; neglected; as, an obsolete word; an obsolete statute; -- applied chiefly to words, writings, or observances.
v. t. & i.
Resolving, or explaining; as, the Resolute Doctor Durand.
a.
Soluble; as, a solute salt.
a.
Viewed apart from modifying influences or without comparison with other objects; actual; real; -- opposed to relative and comparative; as, absolute motion; absolute time or space.
a.
Pure; unmixed; as, absolute alcohol.
a.
Absolute.