Corrections and hints for Assignment 10:

PROBLEM 1: The condition on the norm of f should
read ||f||_{L^1} = 1 .

PROBLEM 2: Correction to Part (b): You need to show that the set 
{ x: d(x,K)=t } has measure zero. 
(This set contains the boundary of K_t).

For every point a with d(x,K)=t, show that the density of 
{ x: d(x,K)<t } at a is at least 1/2. Then apply the Lebesgue
Differentiation Theorem to { x: d(x,K)=t }.