Khinchin–Kolmogorov theorem

E378995

mathematical theorem probability theorem

The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.

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All labels observed (2)

Label	Occurrences
Khinchin–Kolmogorov theorem canonical	2
Kolmogorov three-series theorem	1

Statements (32)

Predicate	Object
instanceOf	mathematical theorem ⓘ probability theorem ⓘ
appliesTo	series of independent random variables ⓘ
assumes	independence of random variables in the series ⓘ
concerns	almost sure convergence ⓘ independent random variables ⓘ series of random variables ⓘ
contrastsWith	convergence in distribution ⓘ convergence in probability ⓘ
field	probability theory ⓘ
hasAspect	conditions on distributions of summands ⓘ conditions on tail probabilities ⓘ conditions on variances or moments ⓘ
hasConvergenceMode	almost sure convergence ⓘ
hasType	convergence theorem ⓘ
historicalPeriod	20th-century mathematics ⓘ
implies	almost sure convergence of the random series under its conditions ⓘ
influenced	development of strong limit theorems ⓘ modern probability theory ⓘ
mathematicalDomain	measure-theoretic probability ⓘ real analysis ⓘ
namedAfter	Aleksandr Khinchin ⓘ Andrei Kolmogorov ⓘ surface form: Andrey Kolmogorov
provides	conditions for almost sure convergence of series of independent random variables ⓘ
relatedTo	Borel–Cantelli lemmas ⓘ Khinchin–Kolmogorov theorem self-linksurface differs ⓘ surface form: Kolmogorov three-series theorem convergence of random series ⓘ almost sure limit theorem ⓘ surface form: strong law of large numbers
usedFor	establishing almost sure convergence criteria ⓘ
usedIn	limit theorems in probability ⓘ stochastic processes ⓘ theory of random series ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Aleksandr Khinchin → notableWork → Khinchin–Kolmogorov theorem ⓘ

Khinchin → notableFor → Khinchin–Kolmogorov theorem ⓘ

subject surface form: Aleksandr Khinchin

Khinchin–Kolmogorov theorem → relatedTo → Khinchin–Kolmogorov theorem self-linksurface differs ⓘ

this entity surface form: Kolmogorov three-series theorem