Posted by A on December 14, 2007, 4:07 pm, in reply to "HW14 #9"
Fix e>0. Let I_y:=(x-e,x+y) and suppose x is a point of density of F. Then lim(|I_y|-|I_y \cap F|)/|I_y|=0 as |I_y|\rightarrow 0. Suppose wlog x,y>0, so |I_y \cap F|\leq y + \delta(x+y). Use |I_y|=y+e and the above to get the result.
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