Symmetric measures on Cartesian products¶
Hewitt, E., & Savage, L. J. (1955). Symmetric measures on Cartesian products. Transactions of the American Mathematical Society.
Cited by¶
1 citation across 1 artifact.
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Domain-specific¶
- Invariant Sigma-Algebra
- In probability, finite-permutation invariance yields the symmetric or exchangeable event sigma-algebra used in the Hewitt–Savage zero-one law for independent identically distributed sequences
This sourceHewitt and Savage define symmetry by invariance under permutations 'leaving all but a finite number of integers fixed', and prove (Theorem 11.3) that a product measure on an infinite product takes only the values 0 and 1 on sets invariant under all finite coordinate permutations. The Hewitt–Savage zero-one law in its original form (Theorem 11.3): under a product measure on an infinite product, every event invariant under all finite permutations of the coordinates has probability zero or one.
SupportedVerified against the source
- In probability, finite-permutation invariance yields the symmetric or exchangeable event sigma-algebra used in the Hewitt–Savage zero-one law for independent identically distributed sequences
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