Lebesgue Integral

★★★★★Graduate+

📖Definition

Integration defined by partitioning range of function. Generalizes Riemann integral

Simple function: ∫φ dμ = Σaᵢ μ(Aᵢ)

General: ∫f dμ = sup∫φ dμ: φ ≤ f, φ simple

MCT, DCT

예제 1

Integral of Dirichlet function

예제 2

∫_ℝ e^{-x²} dx = √π

Probability

Fourier analysis

Function spaces

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