Thread: riemann integrable

A bounded real valued function on [0,1] which is not Riemann Stieljes integrable with respect to $\displaystyle \alpha(x)=x^{2}$

Originally Posted by Chandru1

A bounded real valued function on [0,1] which is not Riemann Stieljes integrable with respect to $\displaystyle \alpha(x)=x^{2}$

What's your question?

give an example

The characteristic function of the rationals.

how can we prove it.

Well, you can always look at the set of discontinuities - that is, if you've already done the criteria for Riemann integrability which says that a function is integrable if and only if its set of discontinuities has measure zero.