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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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