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(2) Let m(E) < o and f be a non-negative measurable function on E such that lim,n S fn exists E and is finite. (i) Show that m({x € E : f(x) > 1}) = 0. (ii) Show that lim, S f" = m({x € E : f(x) = 1}). E

(2) Let m(E) < o and f be a non-negative measurable function on E such that lim,n S fn exists E and is finite. (i) Show that m({x € E : f(x) > 1}) = 0. (ii) Show that lim, S f" = m({x € E : f(x) = 1}). E

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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(2) Let m(E) <o and f be a non-negative measurable function on E such that lim,+ S fn exists E and is finite. (i) Show that m({x € E : f(x) > 1}) = 0. (ii) Show that lim, S f" = m({x € E : f(x) = 1}).
Transcribed Image Text:(2) Let m(E) <o and f be a non-negative measurable function on E such that lim,+ S fn exists E and is finite. (i) Show that m({x € E : f(x) > 1}) = 0. (ii) Show that lim, S f" = m({x € E : f(x) = 1}).
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