fn (x) = Vx e (1, 00), Vn E N. Explain why the sequence {fn} does not satisfy the conclusion of the Lebesgue Dominated Convergence Theorem.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 34E
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Consider the sequence of functions {fn} defined on the interval (1, 0), where
fn(x)
1
Vx E (1, 00), Vn E N.
= -
nx
Explain why the sequence {fn} does not satisfy the conclusion of the Lebesgue
Dominated Convergence Theorem.
Transcribed Image Text:Consider the sequence of functions {fn} defined on the interval (1, 0), where fn(x) 1 Vx E (1, 00), Vn E N. = - nx Explain why the sequence {fn} does not satisfy the conclusion of the Lebesgue Dominated Convergence Theorem.
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