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- Thread starter sutupidmath
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uart

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For that matter neither can a large number or even a countably infinite number of isolated points change the value of an integral. (assuming of course that's there's no nasties like the Dirac Delta "function" involved).

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matt grime

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Yes you can, if the function is bounded on [a, b). And it is equal to the integral of the function [a,b].

This is not true for the Reimann integral, which is why the Reimann integral is utterly worthless, in favor of Lebesgue.For that matter neither can a large number or even a countably infinite number of isolated points change the value of an integral.

For example, the function:

f(x) = {0 if x is irrational, 1 if x is rational}

has only countably many discontinuities, but it not reimann integrable

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No, I'm pretty sure that function is discontinuousFor example, the function:

f(x) = {0 if x is irrational, 1 if x is rational}

has only countably many discontinuities, but it not reimann integrable

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matt grime

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HallsofIvy

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