Linked from

The 45 pages that link to Lebesgue integral, each with the reason it gives.

• Probability density functionRelated: Probability densities are integrated in this measure-theoretic framework.

• Lebesgue measureRelated: Lebesgue measure provides the sizes used to define this integral.

• Probability measureRelated: Expected values are integrals of random variables with respect to probability measures.

• Measure theoryRelated: It extends integration beyond the limits of Riemann integration.

• Real analysisRelated: It extends integration to broader function classes and supports powerful convergence theorems.

• Indicator functionRelated: Integrating an indicator gives the measure of its set.

• Conditional expectationRelated: The defining average identity for conditional expectation uses integration over information sets.

• Hölder's inequalityRelated: The integral version requires a framework for integrating products of measurable functions.

• Lp spaceRelated: It gives the integral of the absolute pth power.

• Almost everywhereRelated: Changing a function on a null set leaves its Lebesgue integral unchanged.

• Fubini's theoremRelated: Its treatment of measurable functions and null sets supplies the standard theorem's framework.

• Measurable functionRelated: Measurability is a central prerequisite for defining this integral.

• Countable additivityRelated: Countable additivity helps ensure the integral behaves correctly under limits and decompositions.

• Harmonic analysisRelated: It supports Fourier analysis for broad classes of functions.

• Lebesgue differentiation theoremRelated: Local integrability makes the averages in the theorem well-defined.

• Measure spaceRelated: It integrates functions on measure spaces beyond the limits of elementary integration.

• Weak solutionRelated: Weak formulations rely on integrals that remain meaningful for nonsmooth functions.

• Radon–Nikodym theoremRelated: Integrating the derivative over a set reconstructs the measure assigned to that set.

• Borel measureRelated: Borel measures supply the set sizes used to define integrals of measurable functions.

• Minkowski inequalityRelated: Its framework defines the integrals appearing in the Lp version.

• Poisson summation formulaRelated: Integrability conditions determine when the sampled sums and Fourier transform are well behaved.

• Hardy–Littlewood maximal functionRelated: The operator averages functions through integrals over measurable neighborhoods.

• Integrable functionRelated: Absolute integrability is defined using this integral in the standard measure-theoretic setting.

• Tonelli's theoremRelated: The theorem concerns Lebesgue integrals, which allow broad measurable domains and infinite values.

• Extended real number lineRelated: Nonnegative Lebesgue integrals naturally take values in the extended real numbers.

• Hahn decomposition theoremRelated: Signed integration is defined through the positive and negative measures the theorem supports.

• Limits of integrationRelated: It broadens integration beyond the familiar interval-and-endpoint setup.