Let for and elsewhere on . Is riemann integrable?

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- June 20th 2009, 08:49 PMChandru1Riemann Integrable Function
Let for and elsewhere on . Is riemann integrable?

- June 21st 2009, 07:23 AMHallsofIvy
Mistaken post. Sorry.

- June 21st 2009, 07:48 AMPlato
Suppose that . That is the set of discontinuities.

is countable so the function is Riemann integrable.

Here is an outline of a proof. In any partition of the subinterval that contains 0 contains almost all points of . The points outside of that can be covered by intervals the sum of their is as small as needed. Thus showing the integral is zero.