# Helly's theorem and piecewise constant function

by muzialis
Tags: constant, function, helly, piecewise, theorem
 P: 152 Hello there, I found in a book a proof of the fact the space of piecewise constant functions with a finite number of jumps is compact, hence a convergent subsequence can be extracted from any bounded sequence. I am wondering , is that not a direct consequence of Helly's Selection Theorem? Indeed, seems to me any piecewise constant function with a finite number of discontinuities belongs to BV locally, which is the requisiste in the aforementioned theorem. Am I worng? Many thanks

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