# Let Un) be a sequence of functions that converges uniformly to I on A and that

**Chapter 8, Problem 24**

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Let Un) be a sequence of functions that converges uniformly to I on A and that satisfiesIIn(x) I ~ M for alln E N and all x EA. If g is continuous on the interval [- M, M], show thatthe sequence (g 0 In) converges uniformly to g 0 I on A.

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