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BRANCH OVERVIEW

Measure theory

Measure sets, integrate functions, and exchange limits safely.

← All branches · Each sheet includes definitions, theorems, applications, and exercises with hints and worked solutions.

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Measure theory

Measure sets, integrate functions, and exchange limits safely.

σ-algebras & measuresNot every subset needs to be measurable; specify the collection on which size is defined.
Lebesgue integration & Lᵖ spacesBuild integrals from measurable simple functions, then identify functions that differ only on null sets.
Convergence theorems & iterated integralsBefore exchanging a limit or order of integration, identify the theorem whose hypotheses apply.