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

^*此作品的通信作者

數學系

研究成果: 書貢獻/報告類型 › 篇章

3 引文斯高帕斯（Scopus）

摘要

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.

原文	英語
主出版物標題	Potentials and Partial Differential Equations
主出版物子標題	The Legacy of David R. Adams
發行者	de Gruyter
頁面	235-264
頁數	30
ISBN（電子）	9783110792720
ISBN（列印）	9783110792652
DOIs	https://doi.org/10.1515/9783110792720-011
出版狀態	已發佈 - 2023 5月 22

ASJC Scopus subject areas

一般數學

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10.1515/9783110792720-011

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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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Some remarks on capacitary integrals and measure theory

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