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Math Help - Can Riemann integrability imply Riemann-Stieltjes integrability, or vice versa?

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    Can Riemann integrability imply Riemann-Stieltjes integrability, or vice versa?

    That is, is it possible that f\in R but f\notin R(\alpha) for some \alpha other than \alpha(x)=x, or f\in R(\alpha) for some \alpha other than \alpha(x)=x, but f\notin R? If it is, can you give me an example? Thanks.
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  2. #2
    Senior Member Shanks's Avatar
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    Riemann integrability does not imply Riemann-Stieltjes integrability,
    and Riemann-Stieltjes integrability does not imply Riemann integrability.
    Rudin's book <<principle of mathematical analysis>> provide a execise as a example in the section on Riemann integral.
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