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Conditional probability in nonstandard analysis. (English) Zbl 0619.60004

In this article the author applies the theory of Loeb measure to conditional probability. First, the author defines and investigates an internal conditional probability P(\(\cdot | A)\), \(A\in^*{\mathfrak B}(V)\), for a hyperfinite probability space \((V,^*{\mathfrak B}(V),P)\) and gives a nonstandard representation for conditional probability \(^{\sim}P(\cdot | A)\), \(A\in {\mathfrak M}(^{\sim}P)\), on the Loeb space (V,\({\mathfrak M}(^{\sim}P),^{\sim}P)\). He then investigates, in a similar manner, conditional expectation E(X\(| {\mathfrak U})\).
Reviewer: R.A.Herrmann

MSC:

60A99 Foundations of probability theory
03H10 Other applications of nonstandard models (economics, physics, etc.)
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