Some remarks on capacitary integrals and measure theory

Augusto C. Ponce; Daniel Spector

doi:10.1515/9783110792720-011

Some remarks on capacitary integrals and measure theory

Augusto C. Ponce^*, Daniel Spector

^*Corresponding author for this work

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

2 Citations (Scopus)

Abstract

We present results for Choquet integrals with minimal assumptions on the monotone set function through which they are defined. They include the equivalence of sublinearity and strong subadditivity independent of regularity assumptions on the capacity, as well as various forms of standard measure theoretic convergence theorems for these nonadditive integrals, e. g., Fatou's lemma and Lebesgue's dominated convergence theorem.

Original language	English
Title of host publication	Potentials and Partial Differential Equations
Subtitle of host publication	The Legacy of David R. Adams
Publisher	de Gruyter
Pages	235-264
Number of pages	30
ISBN (Electronic)	9783110792720
ISBN (Print)	9783110792652
DOIs	https://doi.org/10.1515/9783110792720-011
Publication status	Published - 2023 May 22

Keywords

Evaescence
Inner or outer or zero-capacity regularity
Locally finite
Monotonicty
Semifinite
Strong or finite or countable subadditivity

ASJC Scopus subject areas

General Mathematics

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10.1515/9783110792720-011

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AU - Spector, Daniel

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AB - We present results for Choquet integrals with minimal assumptions on the monotone set function through which they are defined. They include the equivalence of sublinearity and strong subadditivity independent of regularity assumptions on the capacity, as well as various forms of standard measure theoretic convergence theorems for these nonadditive integrals, e. g., Fatou's lemma and Lebesgue's dominated convergence theorem.

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KW - Inner or outer or zero-capacity regularity

KW - Locally finite

KW - Monotonicty

KW - Semifinite

KW - Strong or finite or countable subadditivity

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BT - Potentials and Partial Differential Equations

PB - de Gruyter

ER -

Some remarks on capacitary integrals and measure theory

Abstract

Keywords

ASJC Scopus subject areas

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