Using these 2 facts for integrable functions f, g
for a constant
Prove that any integrable function f can be changed at a finite number of points in the interval [a,b] without changing its integrability or its integral.
Start of Proof
I know that I only have to prove it for changing 1 point, and an induction argument will take care of the rest.
But how do I go about doing this?
I started with the definition of integrability
, where and are partitions of
and so dealing with only the sup and a partition a<x_1<b)" alt="Pa<x_1<b)" /> and a<x_2<b)" alt="Qa<x_2<b)" />
I need to prove
How do I use the given facts to solve this problem. Or do I need a new approach
Thanks in advance.