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(Solved): Measure theory 6.F. If fLp and if En={xX:f(x)n}, then (En)0 as n ...

Measure theory

$6.F. If \( f \in L_{p} \) and if \( E_{n}=\{x \in X:|f(x)| \geqslant n\} \), then \( \mu\left(E_{n}\right) \rightarrow 0 \) a$

6.F. If

f ? L_{p}

and if

E_{n} = {x ? X : ? f (x) ? ? n}

, then

? (E_{n}) ? 0

as

n ? ?

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