Suppose u is a finite Borel measure on R, which is singular to Lebesgue measure. Show that except for a set of Lebesgue measure zero, we have lim "(r -r,x+r]) 2r = 0.
Suppose u is a finite Borel measure on R, which is singular to Lebesgue measure. Show that except for a set of Lebesgue measure zero, we have lim "(r -r,x+r]) 2r = 0.
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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Suppose u is a finite Borel measure on R, which is singular to Lebesgue
measure. Show that except for a set of Lebesgue measure zero, we have
u(-r,x+r)
lim
0.
%3D
2r
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