Let (X, A, ) be a measure space and p belongs to [1, ). : Let...

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Let (X, A, μ) be a measure space and p belongs to [1, ∞). : Let f belongs to LP(X) and (fn neN) C LP(X). Suppose limn-fn- fl|p = 0. Show that for every > 0, there exists >0 such that for all n N we have [fndμ < e for every E € A such that µ(E) < 6. E Let (X, A, μ) be a measure space and p belongs to [1, ∞). : Let f belongs to LP(X) and (fn neN) C LP(X). Suppose limn-fn- fl|p = 0. Show that for every > 0, there exists >0 such that for all n N we have [fndμ < e for every E € A such that µ(E) < 6. E

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