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# Category Archives: Uniform Continuity

## May 1990 #4

Problem Statement: Using properties of the Riemann Integral show that if is Riemann Integrable on and then is uniformly continuous on . Proof: We wish to show that for every there exists a such that for every in it follows that . … Continue reading

Posted in Analysis, Compact, Uniform Continuity
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## Winter 1995 #4

Problem Statement: Let be uniformly continuous and let for every . Show converges uniformly. Proof: First I claim that converges pointwise to . Let . Then . Since is continuous and converges to it follows that . This holds for all … Continue reading

## Fall 1991 #5

This begins my study of sequences and series of functions. These bad boys have a tendency of tripping me up so I’ve decided to spend some quality time learning their ways. Problem Statement: Let and let be a sequence of real-valued functions on … Continue reading

Posted in Analysis, Math, Sequence of Functions, Uniform Continuity
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