SOLVED: Let be a measure on a set , for any 1 p < ∞, define IP(X,)=f: ∫|f|^p dP<∞ and L(S,)=f: ess sup|f|<∞ Prove that for 1 p < ∞, LP(, )
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SOLVED: If f, g are measurable functions, then ess sup (f + g) ≤ ess sup f + ess sup g. Show that for measurable f, ess sup f ≤ sup f.
