The Hewitt-Savage Zero-One Law is a theorem of probability theory stating that any event defined in terms of an infinite sequence of independent, identically distributed random variables, whose occurrence is unaffected by any finite rearrangement of that sequence, must have probability exactly zero or exactly one. Named for Edwin Hewitt and Leonard Jimmie Savage, it is closely related to Kolmogorov's Zero-One Law and to the Borel-Cantelli Lemma, though it applies to a broader class of exchangeable events than Kolmogorov's tail-event version covers.
Facts
StatementAny event determined by the values of an infinite sequence of independent identically distributed random variables and unchanged by finite permutations of the indices has probability either 0 or 1. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Hewitt-Savage zero-one law (Wikipedia)
Sources
1. Hewitt-Savage zero-one law (Wikipedia)
Statement
any event whose occurrence or non-occurrence is determined by the values of these random variables and whose occurrence or non-occurrence is unchanged by finite permutations of the indices, has probability either 0 or 1.
- In Branch: Probability and Statistics, Lead sentence
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