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The set X is a standard measure space when equipped with the smallest standard σ \\sigma -algebra M \\mathfrak {M} containing the algebra A \\mathcal {A} , where the extended real-valued measure μ \\mu on M \\mathfrak {M} is generated by the standard part of ν \\nu . If f is A \\mathcal {A} -measurable, then its standard part 0 f ^0f is M \\mathfrak {M} -measurable on X . If f and μ \\mu are finite, then the ν \\nu -integral of f is infinitely close to the μ \\mu -integral of 0 f ^0f . Applications include coin tossing and Poisson processes. 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Conversion from nonstandard to standard measure spaces and applications in probability theory 论文

Conversion from nonstandard to standard measure spaces and applications in probability theory · 相关技术

相关技术