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Construction of a Probability Measure

Authors :
Jean Jacod
Philip Protter
Source :
Universitext ISBN: 9783540438717, Universitext ISBN: 9783540664192
Publication Year :
2004
Publisher :
Springer Berlin Heidelberg, 2004.

Abstract

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.

Details

ISBN :
978-3-540-43871-7
978-3-540-66419-2
ISBNs :
9783540438717 and 9783540664192
Database :
OpenAIRE
Journal :
Universitext ISBN: 9783540438717, Universitext ISBN: 9783540664192
Accession number :
edsair.doi.dedup.....a907d7902ca4ba566bc743442dcf21d1
Full Text :
https://doi.org/10.1007/978-3-642-55682-1_6