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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

2 votes
0 answers
64 views

Measure of the convex hull of a ball and a point

I need to prove the following statement: Let $B_s(z)$ be a ball centered at $z$ of radius $s$ s.t. $0\not\in B_s(z)$. Moreover let $K_s(z)$ the convex hull of $\{0\}\cup B_s(z)$. Then $$ \l …
A. Ninno's user avatar
1 vote
0 answers
60 views

Perimeter decreases under intersection with half spaces

The main thing i need to prove is the following assertion: Let $E\subset R^N$ be a set of finite perimeter and $H=\{x\in R^N : x\cdot e < t \}$ for $t\in R$ and $e\in S^{N-1}$. Then prove that $$ \t …
A. Ninno's user avatar