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Borel probability law on a polish space
Definition
Let S be Polish in the sense of Polish spaces are separable completely metrizable spaces. A Borel probability law on S is a countably additive measure on with total mass one. Here is The Borel sigma-algebra of a topological space and probability measure means Probability measures and probability spaces. A compatible complete metric may be fixed for a construction; it is not additional data in the law. The empty space admits no such law, since its measure must be both zero and one.
Depends on
Used by
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Sources
- van Gaans, §2, p. 3 (standard reference, not scraped)