Lp Convergence

#MeasureTheory >[!def] LpL^{p} Convergence fn→f in Lpf_{n}\to f\text{ in }L^{p} if ∥fn−f∥Lp→0\|f_{n}-f\|_{L^p}\to0

Remark

LpL^{p} convergence   ⟹   μ\implies \ \mu-a.s. convergence.

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