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 | |
| 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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