Displaying similar documents to “On regular conditional probabilities”

Extensions of set functions.

Sergei V. Ovchinnikov, Jean Claude Falmagne (2003)

Mathware and Soft Computing

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We establish a necessary and sufficient condition for a function defined on a subset of an algebra of sets to be extendable to a positive additive function on the algebra. It is algo shown that this condition is necessary and sufficient for a regular function defined on a regular subset of the Borel algebra of subsets of a given compact Hausdorff space to be extendable to a measure.

Equivalent or absolutely continuous probability measures with given marginals

Patrizia Berti, Luca Pratelli, Pietro Rigo, Fabio Spizzichino (2015)

Dependence Modeling

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Let (X,A) and (Y,B) be measurable spaces. Supposewe are given a probability α on A, a probability β on B and a probability μ on the product σ-field A ⊗ B. Is there a probability ν on A⊗B, with marginals α and β, such that ν ≪ μ or ν ~ μ ? Such a ν, provided it exists, may be useful with regard to equivalent martingale measures and mass transportation. Various conditions for the existence of ν are provided, distinguishing ν ≪ μ from ν ~ μ.

The Relevance of Measure and Probability, and Definition of Completeness of Probability

Bo Zhang, Hiroshi Yamazaki, Yatsuka Nakamura (2006)

Formalized Mathematics

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In this article, we first discuss the relation between measure defined using extended real numbers and probability defined using real numbers. Further, we define completeness of probability, and its completion method, and also show that they coincide with those of measure.