# Function integrable proof

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Let f: [a,b] mapped onto Reals be a nonnegative function that is integrable over [a,b]. Then the integral from a to b of f = 0 if and only if greatest lower bound of f (I) = 0 for each open interval I in [a,b].

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Please see the attachment.

Let f: [a,b] mapped onto Reals be a nonnegative function that is integrable over [a,b]. Then the integral from a to b of f = 0 if and only if greatest lower bound of f (I) = 0 for each open interval I in [a,b].

Proof. By the hypothesis, we know that for all .

If , ...

#### Solution Summary

This describes a function mapped onto the real numbers that is integrable, and uses this fact to prove a related function is integrable.

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