Egoroff’s Theorem and Lusin’s Theorem for Capacities in the Framework of - Expectation

Zhaojun Zong, Feng Hu and Xiaoxin Tian

Mathematical Problems in Engineering, 2020, vol. 2020, 1-7

Abstract:

In the classical real analysis theory, Egoroff’s theorem and Lusin’s theorem are two of the most important theorems. The σ -additivity of measures plays a crucial role in the proofs of these theorems. Later, many researchers have carried out lots of studies on Egoroff’s theorem and Lusin’s theorem when the measure is monotone and nonadditive (see, e.g., Li and Yasuda (2004) and Li and Mesiar (2011)). In this paper, we study Egoroff’s theorem and Lusin’s theorem for capacities in the framework of - expectation. We give some different assumptions that provide Egoroff’s theorem and Lusin’s theorem in the framework of - expectation.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:1450486

DOI: 10.1155/2020/1450486

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