View source for Problem set 11: gotta push, its fourth quarter.. who wants it more OldKiwi - Rhea

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Please post solutions here.

I believe 5(b) is false, as demonstrated by the counterexample <math>f(x)=\sum n\chi_{[n,n+\frac{1}{n^3}]}</math>.  By Lebesgue's Differentiation Theorem, <math>f^*(x)\geq f(x)</math> a.e.  So <math>f^*(x)</math> is unbounded outside any compact set.  -pete