(4) Let (fn)n>o be a sequence of bounded functions on EC R. This means that for each n, there exists a positive real num

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4 Let Fn N O Be A Sequence Of Bounded Functions On Ec R This Means That For Each N There Exists A Positive Real Num 1 (22.38 KiB) Viewed 10 times

(4) Let (fn)n>o be a sequence of bounded functions on EC R. This means that for each n, there exists a positive real number M₁ such that fn(x)| ≤ Mn for all x € E. Show that if (fn)n>o is uniformly convergent, then there exists a positive real number M such that |fn(x) < M for all n > 0 and all x € E.