(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm looking for a sequence of simple functions f_{n}that converges uniformly to f(x)=x^{2}on the interval [0,1].

2. Relevant equations

I know a simple function is one that can be written as [itex]\sum^{n}_{k=1}a_{k}1_{D_{k}}(x)[/itex] where {D_{1},...,D_{n}} is collection of measurable sets and a_{1},...,a_{n}are real numbers.

3. The attempt at a solution

I don't really know how to begin here. My general idea would be to break up the range of the function into pieces, take the inverse image of these pieces and make these the D's, the measurable sets whose characteristic functions we are looking at. The a's, the actual values that the simple function takes on, could be the smallest value in a particular piece of the range. The higher terms of the sequence would break the range into smaller and smaller pieces.

But how would I actually write down this sequence of functions?

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# Homework Help: Approximating x^2 as a sequence of simple functions

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