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Construction of a Probability Measure
- 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