Nonadditive measures and nonlinear integrals —focusing on a theoretical aspect—

Kawabe, Jun

doi:10.1090/suga/458

Nonadditive measures and nonlinear integrals —focusing on a theoretical aspect—
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by Jun Kawabe
Translated by: the author

Sugaku Expositions 34 (2021), 61-92

DOI: https://doi.org/10.1090/suga/458

Published electronically: April 28, 2021

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Abstract:

Nonadditive measures are monotonically increasing set functions that are not necessarily additive and nonlinear integrals are the integrals with respect to nonadditive measures. The main theme of the theoretical study of nonadditive measures and nonlinear integrals is the refinement of measure theory and is accomplished by finding necessary and sufficient conditions (or sufficient conditions weak enough) under which various important theorems in measure theory remain valid for nonadditive measures. In this expository article, some of the basic results are described in exact detail in terms of refining measure theory, each of which is the cornerstone of developing the study of nonadditive measures and nonlinear integrals.

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