Erschienen in:

2004 | OriginalPaper | Buchkapitel

Construction of a Probability Measure

verfasst von : Jean Jacod, Philip Protter

Erschienen in: Probability Essentials

Verlag: Springer Berlin Heidelberg

Enthalten in: Professional Book Archive

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Here we no longer assume Ω is countable. We assume given Ω and a σ-algebra A⊂(2Ω. (Ω, A) is called a measurable space. We want to construct probability measures on A. When Ω is finite or countable we have already seen this is simple to do. When Ω is uncountable, the same technique does not work; indeed, a “typical” probability P wih have P({ω|)=0 for all ω, and thus the family of all numbers P({ω|) for ω∈Ω does not characterize the probability P in general.

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