On Differentiation of Integrals With Respect to Bases of Convex Sets

A. M. Stokolos

doi:10.4064/sm-119-2-99-108

On Differentiation of Integrals With Respect to Bases of Convex Sets

A. M. Stokolos

Mathematical Sciences

Odessa National University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Differentiation of integrals of functions from the class Lip (1,1) ( I 2 ) with respect to the basis of convex sets is established. An estimate of the rate of differentiation is given. It is also shown that there exist functions in Lip (1,1) ( I N ) , N ≥ 3, and H ω 1 ( I 2 ) with ω(δ)/δ → ∞ as δ → +0 whose integrals are not differentiated with respect to the bases of convex sets in the corresponding dimension.

Original language	American English
Journal	Studia Mathematica
Volume	119
DOIs	https://doi.org/10.4064/sm-119-2-99-108
State	Published - 1996

Disciplines

Mathematics

Keywords

Bases of Convex Sets
Differentiation of Integrals

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title = "On Differentiation of Integrals With Respect to Bases of Convex Sets",

abstract = " Differentiation of integrals of functions from the class Lip (1,1) ( I 2 ) with respect to the basis of convex sets is established. An estimate of the rate of differentiation is given. It is also shown that there exist functions in Lip (1,1) ( I N ) , N ≥ 3, and H ω 1 ( I 2 ) with ω(δ)/δ → ∞ as δ → +0 whose integrals are not differentiated with respect to the bases of convex sets in the corresponding dimension. ",

keywords = "Bases of Convex Sets, Differentiation of Integrals",

author = "Stokolos, \{A. M.\}",

note = "Conference on functional analysis (September 4-10, 1960, Warsaw) S. Mazur Studia Mathematica (1963), 1-6 DOI: 10.4064/sm-Special Series-1-1-6",

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doi = "10.4064/sm-119-2-99-108",

language = "American English",

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journal = "Studia Mathematica",

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T1 - On Differentiation of Integrals With Respect to Bases of Convex Sets

AU - Stokolos, A. M.

N1 - Conference on functional analysis (September 4-10, 1960, Warsaw) S. Mazur Studia Mathematica (1963), 1-6 DOI: 10.4064/sm-Special Series-1-1-6

PY - 1996

Y1 - 1996

N2 - Differentiation of integrals of functions from the class Lip (1,1) ( I 2 ) with respect to the basis of convex sets is established. An estimate of the rate of differentiation is given. It is also shown that there exist functions in Lip (1,1) ( I N ) , N ≥ 3, and H ω 1 ( I 2 ) with ω(δ)/δ → ∞ as δ → +0 whose integrals are not differentiated with respect to the bases of convex sets in the corresponding dimension.

AB - Differentiation of integrals of functions from the class Lip (1,1) ( I 2 ) with respect to the basis of convex sets is established. An estimate of the rate of differentiation is given. It is also shown that there exist functions in Lip (1,1) ( I N ) , N ≥ 3, and H ω 1 ( I 2 ) with ω(δ)/δ → ∞ as δ → +0 whose integrals are not differentiated with respect to the bases of convex sets in the corresponding dimension.

KW - Bases of Convex Sets

KW - Differentiation of Integrals

UR - https://doi.org/10.4064/sm-119-2-99-108

U2 - 10.4064/sm-119-2-99-108

DO - 10.4064/sm-119-2-99-108

M3 - Article

SN - 0039-3223

VL - 119

JO - Studia Mathematica

JF - Studia Mathematica

ER -

On Differentiation of Integrals With Respect to Bases of Convex Sets

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