Lp Convergence

#MeasureTheory >[!def] LpL^{p} Convergence fnf in Lpf_{n}\to f\text{ in }L^{p} if fnfLp0\|f_{n}-f\|_{L^p}\to0

Remark

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

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