Give an example of a sequence of continuous functions: fn : [0, 1] →R that converges pointwise to 0 on [0, 1] but no subsequence of fn converges uniformly on any subinterval of (0, 1].
Give an example of a sequence of continuous functions: fn : [0, 1] →R that converges pointwise to 0 on [0, 1] but no subsequence of fn converges uniformly on any subinterval of (0, 1].
Give an example of a sequence of continuous functions: fn : [0, 1] →R that converges pointwise to 0 on [0, 1] but no subsequence of fn converges uniformly on any subinterval of (0, 1].
Transcribed Image Text:Give an example of a sequence of continuous functions: fn : [0, 1] → R that converges
pointwise to 0 on [0, 1] but no subsequence of fn converges uniformly on any subinterval
of [0, 1].
Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.
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![Give an example of a sequence of continuous functions: fn : [0, 1] → R that converges
pointwise to 0 on [0, 1] but no subsequence of fn converges uniformly on any subinterval
of [0, 1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80fac62b-1f91-4b94-88b2-6d2c841a4645%2F095fd5a5-d79e-4441-aad4-e87da839853c%2F17xhyc_processed.png&w=3840&q=75)
