Let S be a closed n-cube with v(S) > 0. Suppose (fk)keN is a sequence of functions from S to R, each bounded and integrable on S. Suppose in addition that (fk)kɛN Converges uniformly on S to ƒ : S → R. Prove that f is bounded and integrable on S.
Let S be a closed n-cube with v(S) > 0. Suppose (fk)keN is a sequence of functions from S to R, each bounded and integrable on S. Suppose in addition that (fk)kɛN Converges uniformly on S to ƒ : S → R. Prove that f is bounded and integrable on S.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 25E: 25. Let, where and are non empty, and let and be subsets of .
Prove that.
Prove that.
Prove...
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![Let S be a closed n-cube with v(S) > 0. Suppose (fk)kEN is a sequence of functions
#5
from S to R, each bounded and integrable on S. Suppose in addition that (fr)kɛN Converges
uniformly on S to f : S → R. Prove that f is bounded and integrable on S.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09caa562-c0c8-4a11-85df-abb5e549e1a9%2F57adaa2e-0414-4864-a184-dea9ba946ccb%2Fqyngzlv_processed.png&w=3840&q=75)
Transcribed Image Text:Let S be a closed n-cube with v(S) > 0. Suppose (fk)kEN is a sequence of functions
#5
from S to R, each bounded and integrable on S. Suppose in addition that (fr)kɛN Converges
uniformly on S to f : S → R. Prove that f is bounded and integrable on S.
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