Some remarks on capacitary integrals and measure theory

Augusto C. Ponce*, Daniel Spector

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)


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 languageEnglish
Title of host publicationPotentials and Partial Differential Equations
Subtitle of host publicationThe Legacy of David R. Adams
Publisherde Gruyter
Number of pages30
ISBN (Electronic)9783110792720
ISBN (Print)9783110792652
Publication statusPublished - 2023 May 22


  • 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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