Lebesgue Measure

★★★★☆Undergraduate

📖Definition

Generalized notion of "size" for sets in ℝⁿ. Overcomes limitations of Riemann integral

Interval measure: λ([a,b]) = b - a

Countable additivity: λ(∪Aₙ) = Σλ(Aₙ) (disjoint)

Outer measure: λ*(A) = infΣℓ(Iₙ): A ⊆ ∪Iₙ

예제 1

λ(ℚ ∩ [0,1]) = 0

예제 2

λ(Cantor set) = 0

Integration

Probability

Fourier analysis

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