# Convergence of elementary function to continuous one. HEEEEELLLPP

• Jul 16th 2012, 08:46 AM
danrioo
Convergence of elementary function to continuous one. HEEEEELLLPP
Hi I have something that I have been trying to prove for a while but can't! I just can't go about using the strange definition of the elementary function to prove the convergence. The book i'm reading simply states the result without much thought, but I can't get it!

g(t) is a continuous function on an interval [a,b] that is bounded (i don't think the fact that it is bounded is used but...)
define an elementary function gn(t) = sum(over i) g(i/2n) 1[i/2, (i+1)/2n)

I want to show that g --> g pointwise on the interval [a,b] I think that the boundedness might give uniform convergence?

any help would be SOOOOOOOOOOOOOO helpful. The definition of the elementary function makes it very confusing to try to go about showing this.
• Jul 16th 2012, 10:52 AM
danrioo
Re: Convergence of elementary function to continuous one. HEEEEELLLPP
If the above seems ambiguous, I am trying to see why the proof that goes along with equation 19.5 here is true: http://www.stat.cmu.edu/~cshalizi/75...lecture-19.pdf
• Jul 16th 2012, 05:55 PM
danrioo
Re: Convergence of elementary function to continuous one. HEEEEELLLPP
PLEASE HEEEEELP :( i guess it's summer and people are taking time off the forum?