DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-13

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

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The finite product of finite probability spaces

Definition

Let $((Ω_{i}, w_{i}))_{i \in I}$ be a finite indexed family of finite probability spaces. Their product probability space has outcome set $Ω : = \prod_{i \in I} Ω_{i}$ and assigns $ω = (ω_{i})_{i \in I}$ the weight $w (ω) : = \prod_{i \in I} w_{i} (ω_{i}) .$ For $I = \emptyset$ , the product outcome set is the singleton containing the empty function and its weight is the empty product $1$ . Normalization and independence of coordinate events are proved in Product weights normalize, and coordinate events are mutually independent ↗.

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Used by

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Sources

C. M. Grinstead and J. L. Snell, Introduction to Probability, 2nd ed., Definitions 4.3-4.5 (standard reference, not scraped)
H. Pishro-Nik, Introduction to Probability, Statistics, and Random Processes, Section 1.4.1 (standard reference, not scraped)