(a) If (fk) is a bounded sequence in M[a, b] and fk f a.e., show that...
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(b) If (gk) is any sequence in M[a, b] and if fk := Arctan ο gk, show that (fk) is a bounded sequence in M[a, b].
(c) If (gk) is a sequence in M[a, b] and if gk → g a.e., show that g ∈ M[a, b].
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a Since f k Ma b is bounded it belongs to R a b The Dominated Convergence Theorem implies that f ...View the full answer
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Related Book For
Introduction to Real Analysis
ISBN: 978-0471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
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