For a sequence of independent random variables, any event determined only by the sequence's tail behavior, unaffected by any finite number of initial terms, has probability either exactly zero or exactly one. Proved by Andrey Kolmogorov, it is a foundational structural fact of probability theory.
Facts
StatementFor a sequence of independent random variables, or more generally a sequence of independent sigma-algebras, any tail event, one whose occurrence does not depend on any finite initial segment of the sequence, has probability exactly zero or exactly one. 1 Classification
Statement Form Connections
Has Statement Form
In Branch
Named After
Sources
1. Kolmogorov's Zero-One Law (Wikipedia)
Wikimedia Foundationlead section, first paragraph
In probability theory, Kolmogorov's zero-one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, namely a tail event of independent σ-algebras, will either almost surely happen or almost surely not happen; that is, the probability of such an event occurring is zero or one.
In Group: Probability Theory, Article text
In probability theory, Kolmogorov's zero-one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, namely a tail event of independent σ-algebras, will either almost surely happen or almost surely not happen; that is, the probability of such an event occurring is zero or one.
View the Source Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.