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The 16 pages that link to Measurable function, each with the reason it gives.

• Random variableBroader topic: This condition ensures that events defined by random-variable values have probabilities.

• Lebesgue integralBroader topic: Measurability ensures the function's level sets can be measured.

• Conditional expectationRelated: Conditional expectations must be measurable with respect to the information they represent.

• Hölder's inequalityRelated: Measurability makes the functions and products in integral forms well-defined.

• Lp spaceRelated: Only measurable functions are eligible for the integral defining Lp.

• Fubini's theoremRelated: Measurability is required for the product-space and iterated integrals in the theorem.

• Dominated convergence theoremRelated: Measurability makes the functions and their limit eligible for Lebesgue integration.

• Measure spaceRelated: Measurability makes functions compatible with integration and measure-based probability.

• Radon–Nikodym theoremRelated: The density supplied by the theorem must be measurable.

• Filtration (probability theory)Related: Measurability determines whether a random variable is observable at a filtration stage.

• Integrable functionNarrower topic: Measurability is required before the Lebesgue integral of the absolute value is defined.

• Real-valued functionRelated: Measurability makes real-valued functions suitable for integration and probability theory.

• Tonelli's theoremNarrower topic: Measurability is one of the theorem's essential hypotheses.

• Random vectorRelated: Measurability makes probabilities of vector-valued events well-defined.

• Lebesgue decomposition theoremRelated: The density of the absolutely continuous component must be measurable.

• Fatou's lemmaNarrower topic: Measurability ensures the pointwise lower limit and tail infima can be integrated.