Register to reply

Helly's theorem and piecewise constant function

by muzialis
Tags: constant, function, helly, piecewise, theorem
Share this thread:
muzialis
#1
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 Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100

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