The Key Theorem of Learning Theory with Samples Corrupted by Equality-Expect Noise on Quasi-Probability Space

Ha, Ming-Hu; Erling, Du; Feng, Zhi-fang; Bai, Yun-Chao

doi:10.1109/icmlc.2006.258981

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“…Sugeno measure is a generalization of probability measure. It was widely used by many scholars such as, Sugeno [5], Minghu Ha [6][7], Chunqin Zhang [8]. In classical measure theory [9], Borel-Cantelli lemma is a fundamental result and is instrumental in proving the strong law of large numbers.…”

Section: Introductionmentioning

confidence: 99%

Borel-Cantelli Lemma for Sugeno Measure

Zhang

2014

AMM

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Sugeno measure is a fuzzy measure. In this paper, we derive the Borel-Cantelli lemma for Sugeno measure. This result is a natural extension of the classical Borel-Cantelli lemma to the case where the measure tool is fuzzy. The properties of Sugeno measure are further discussed. Then the Borel-Cantelli lemma will be proven on Sugeno measure space. This work generalizes the research and applications of the Borel-Cantelli lemma.

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