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 g_{n}(t) = sum(over i) g(i/2^{n}) 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.