Register to reply

Helly's theorem and piecewise constant function

by muzialis
Tags: constant, function, helly, piecewise, theorem
Share this thread:
Feb27-12, 09:39 AM
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
Phys.Org News Partner Science news on
'Smart material' chin strap harvests energy from chewing
King Richard III died painfully on battlefield
Capturing ancient Maya sites from both a rat's and a 'bat's eye view'

Register to reply

Related Discussions
Give me a function that is piecewise continuous but not piecewise smooth Calculus 5
4th order linear, with constant piecewise coefficients Differential Equations 1
Helly's Selection Theorem Calculus & Beyond Homework 0
Find a formula for a constant function using the mean value theorem Calculus & Beyond Homework 1
Finding constants in a piecewise function that allow the function to be differentiabl Calculus & Beyond Homework 5