Problem 13 in Chapter 7 of baby Rudin states:(adsbygoogle = window.adsbygoogle || []).push({});

Assume [tex]\{f_n\}[/tex] is a sequence of monotonically increasing functions on R with [tex]0 \leq f_n(x) \leq 1[/tex] for all x and all n.

(a) Prove that there is a function f and a sequence [tex]\{n_k\}[/tex] such that [tex]f(x) = \lim_{k \rightarrow \infty}f_{n_k}(x)[/tex] for every x in R.

(b) If, moreover, f is continuous, prove that [tex]f_{n_k} \rightarrow f[/tex] uniformly on R.

Anyone else notice a problem with (b)?

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# Another nontrivial (trick) question in Chapter 7

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