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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].

For that matter neither can a large number or even a countably infinite number of isolated points change the value of an integral.

This is not true for the Reimann integral, which is why the Reimann integral is utterly worthless, in favor of Lebesgue.

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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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

No, I'm pretty sure that function is discontinuous

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matt grime

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HallsofIvy

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