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