Measure and Integration
Explore measurable structures; functions and convergence; product spaces and densities. Concepts and connections are available independently of video coverage.
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Sigma-algebras
A sigma-algebra is closed under complements and countable unions.
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Lebesgue measure
Lebesgue measure extends interval length to a complete measure on a class of real sets.
Measurable functions
Inverse images of appropriate Borel sets must be measurable.
Measures
A measure assigns nonnegative size and is countably additive on disjoint measurable sets.
Sets
A set is a collection of distinct objects; membership is different from inclusion.
Almost everywhere
A property holds almost everywhere if its exceptional set has measure zero.
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