Show that for every parameter > 0 > 0 the function x ( sin
Question:
Show that for every parameter α>0 the function
x↦(sinxx)3e−αx
is integrable over (0,∞) and that the integral is continuous as a function of the parameter. [ find piecewise integrable majorants like in Problem 12.18 ; use the continuity lemma.]
Data from problem 12.8
Transcribed Image Text:
Let A denote Lebesgue measure on R". (i) Let u L (A) and KCR" be a compact (i.e. closed and bounded) set. Show that limx SK+x|f|dx=0. (ii) Let u be uniformly continuous and fPEL(A) for some p>0. Show that limx f(x) = 0.
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