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(6) Let {fn} be a sequence of measurable functions. We say that fn tends to f in measure if for any a > 0 lim μ({x: |fn(x) − f(x)| > a}) = 0. 818 (a) Is it true that ||fn - fl|p → 0 implies fn tends to f in measure? (b) Is it true that få tends to ƒ in measure implies || fn – ƒ ||p → 0.

(6) Let {fn} be a sequence of measurable functions. We say that fn tends to f in measure if for any a > 0 lim μ({x: |fn(x) − f(x)| > a}) = 0. 818 (a) Is it true that ||fn - fl|p → 0 implies fn tends to f in measure? (b) Is it true that få tends to ƒ in measure implies || fn – ƒ ||p → 0.

Advanced Engineering Mathematics
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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(6) Let {f} be a sequence of measurable functions. We say that fn tends to f in measure if for any a > 0 lim µ({x: |fn(x) - f(x)| > a}) = 0. 81x (a) Is it true that ||ƒn − ƒ||p → 0 implies ƒ tends to ƒ in measure? (b) Is it true that fn tends to ƒ in measure implies ||fn - ƒ||p → 0.
Transcribed Image Text:(6) Let {f} be a sequence of measurable functions. We say that fn tends to f in measure if for any a > 0 lim µ({x: |fn(x) - f(x)| > a}) = 0. 81x (a) Is it true that ||ƒn − ƒ||p → 0 implies ƒ tends to ƒ in measure? (b) Is it true that fn tends to ƒ in measure implies ||fn - ƒ||p → 0.
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