Given $f : [0, 1] \rightarrow \mathbb{R}$ be a bounded function which is continuous on $[0,1]$ except at $1/2$. Let $\alpha(x) = x^2$. No further description of function $f$ is given. How do I show that $f$ Riemann Stieltjes integrable with respect to $\alpha$?
2026-04-06 13:09:10.1775480950
Show that $f$ is Riemann Stieltjes integrable?
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It follows from the equality $$(R-S)\int_0^1 fdg =(R)\int_0^1 f(x)\alpha'(x) dx$$