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Relation among continuous functions
δ may depend on ε and ƒ. For pointwise equicontinuity, δ may depend on ε and x0. For uniform equicontinuity, δ may depend only on ε. More generally,
Equicontinuity
in Probability and Stochastic Equicontinuity" (PDF). 30 August 2010. Hagemann, Andreas (2014). "Stochastic equicontinuity in nonlinear time series models"
Stochastic_equicontinuity
On when a family of real, continuous functions has a uniformly convergent subsequence
interval has a uniformly convergent subsequence. The main condition is the equicontinuity of the family of functions. The theorem is the basis of many proofs
Arzelà–Ascoli_theorem
Linear map from a vector space to its field of scalars
In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars
Linear_form
In mathematics, especially functional analysis, a bornology B {\displaystyle {\mathcal {B}}} on a vector space X {\displaystyle X} over a field K , {\displaystyle
Vector_bornology
Gives condition for a set of functions to be relatively compact in an Lp space
{\displaystyle B} ). However, it has been shown that equitightness and equicontinuity imply this property. For a subset B {\displaystyle B} of L p ( Ω ) {\displaystyle
Fréchet–Kolmogorov_theorem
kernel K yields a compact operator. Compactness may be shown by invoking equicontinuity, and more specifically the theorem of Arzelà-Ascoli. As an operator
Fredholm_integral_equation
Jewish-Italian mathematician (1843–1896)
real variable and to Fourier series. For example, Ascoli introduced equicontinuity in 1884, a topic regarded as one of the fundamental concepts in the
Giulio_Ascoli
Mathematical function with no sudden changes
(mathematics) Absolute continuity Approximate continuity Dini continuity Equicontinuity Geometric continuity Parametric continuity Classification of discontinuities
Continuous_function
Set of functions between two fixed sets
Clifford algebra Tensor field Spectral theory Functional determinant Equicontinuity Ascoli's theorem Lang, Serge (1987). "Linear Algebra". Undergraduate
Function_space
Statistical estimator
extremum estimator), then a more complicated argument involving stochastic equicontinuity has to be used. An estimator can be unbiased but not consistent. For
Consistent_estimator
Romanian-American mathematician (1935–2025)
Tulcea, Alexandra (1973). "On pointwise convergence, compactness and equicontinuity in the lifting topology I". Zeitschrift für Wahrscheinlichkeitstheorie
Alexandra_Bellow
discontinue, discontinuity, discontinuous, entertain, entertainment, equicontinuity, equicontinuous, impertinence, impertinent, incontinence, incontinent
List of Greek and Latin roots in English/P–Z
List_of_Greek_and_Latin_roots_in_English/P–Z
American economist
JSTOR 2938351. — (1991). "Uniform Convergence in Probability and Stochastic Equicontinuity". Econometrica. 59 (4): 1161–1167. doi:10.2307/2938179. JSTOR 2938179
Whitney_K._Newey
Type of polynomial used in Numerical Analysis
of functions with a set of Bernstein polynomials in the context of equicontinuity. The probabilistic proof can also be rephrased in an elementary way
Bernstein_polynomial
Field of mathematics
algebraic closure Cp. The metric on K and the standard definition of equicontinuity leads to the usual definition of the Fatou and Julia sets of a rational
Arithmetic_dynamics
SETAR model as a limiting case by showing the uniform boundedness and equicontinuity with respect to the switching parameter. Without this proof, to say
STAR_model
differential equation Stochastic dominance Stochastic drift Stochastic equicontinuity Stochastic gradient descent Stochastic grammar Stochastic investment
List_of_statistics_articles
Notion in metric geometry
(Follows from every extremal function on X being 1-Lipschitz; cf. Equicontinuity#Examples.) Not every Katetov function on X is extremal. For example
Tight_span
discontinue, discontinuity, discontinuous, entertain, entertainment, equicontinuity, equicontinuous, impertinence, impertinent, incontinence, incontinent
List of Greek and Latin roots in English/T
List_of_Greek_and_Latin_roots_in_English/T
of Michigan. OCLC 68274401. Clay, Jesse Paul (1961). Proximity and equicontinuity in transformation groups. Philadelphia, PA: University of Pennsylvania
List of African-American mathematicians
List_of_African-American_mathematicians
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