Linked from

The 27 pages that link to Sigma-algebra, each with the reason it gives.

• Lebesgue measureNarrower topic: Lebesgue measure is defined on a sigma-algebra of subsets.

• Power setBroader topic: It selects measurable collections from the full power set of a space.

• Probability measureRelated: It specifies which subsets of the sample space count as measurable events.

• Measure theoryRelated: It specifies which sets a measure is allowed to assign sizes.

• Probability spaceRelated: It determines which subsets of outcomes qualify as events.

• Conditional expectationBroader topic: A sigma-algebra formalizes exactly which information the conditional expectation may use.

• Sample spaceRelated: Infinite probability models often restrict events to a sigma-algebra of subsets.

• Event (probability theory)Related: Only subsets in this collection are measurable events.

• Measurable functionNarrower topic: It specifies which domain and codomain subsets count as measurable.

• Countable additivityRelated: A measure is defined on a sigma-algebra, which contains the unions required by countable additivity.

• Measure spaceRelated: It specifies exactly which subsets can receive a measure.

• Radon–Nikodym theoremRelated: Measures and measurable densities are defined relative to σ-algebras.

• Borel measureNarrower topic: The Borel sets form a sigma-algebra, which makes countable measure operations well-defined.

• MartingaleNarrower topic: A filtration consists of sigma-algebras that encode the process’s available information.

• Filtration (probability theory)Narrower topic: Each stage of a filtration is a sigma-algebra of events known by that time.

• Independent random variablesRelated: General independence is defined through factorization of probabilities for events in generated sigma-algebras.

• Nonmeasurable setRelated: Membership in the sigma-algebra is the criterion for measurability in a measure space.

• Tonelli's theoremRelated: It specifies which subsets in each factor space are measurable.

• Probability axiomsRelated: Probability is defined only for events in the model's sigma-algebra.

• Carathéodory's extension theoremNarrower topic: This is the larger domain on which the extended measure is defined.

• Kolmogorov extension theoremRelated: The theorem's probability measure is defined on a sigma-algebra generated by coordinate events.

• Law of total varianceRelated: It formalizes the information on which conditional means and variances depend.

• Doob martingaleNarrower topic: Filtrations are built from sigma-algebras, which determine what can be known at each stage.

• Kolmogorov's zero–one lawNarrower topic: The tail σ-algebra is a particular σ-algebra, and the law concerns probabilities of its events.

• Dynkin systemCompared with: Unlike a Dynkin system, it need not restrict countable unions to disjoint families.

• Hahn decomposition theoremRelated: Both pieces of the decomposition must be measurable.

• Ibragimov–Iosifescu conjectureRelated: Mixing coefficients compare information represented by past and future sigma-algebras.