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## Homework Statement

## Homework Equations

## The Attempt at a Solution

I'm pretty clueless as to what's going on here. If someone can just please lead me in the right direction, I would be quite grateful.

- Thread starter varygoode
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I'm pretty clueless as to what's going on here. If someone can just please lead me in the right direction, I would be quite grateful.

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Dick

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But how do I generalize this?

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Dick

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So for every epsilon > 0 there exists delta > 0 s.t. |x-y|< delta implies |f(x) - f(y)| < epsilon. I've got that I think.

But I need something else to connect that and the rectangles. I'm horrible at picturing things, so that won't help. I'm just not sure how to define the rectangles in order to ensure they cover G(f). I simply don't see it.

What is the connection?

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Dick

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Draw rectangles that are delta in x by epsilon in y in size. How many do you need to cover the range of x in [0,1]? Multiply that by the area of each one. You are right on the uniform thing.

Last edited:

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Can you give me this explanation in some mathematically explicit terms? I'm having trouble following what's going on here.

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Dick

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