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Keywords:
Kurzweil-Stieltjes integral; Hölder function; counterexample
Kurzweil-Stieltjes integral; Hölder function; counterexample
Summary:
For any $\alpha , \beta >0$ with $\alpha +\beta <1$ we provide a simple construction of an $\alpha $-Hölde function $f\colon [0,1]\to {\mathbb R}$ and a $\beta $-Hölder function $g\colon [0,1]\to {\mathbb R}$ such that the integral $\int _0^1 f {\rm d} g$ fails to exist even in the Kurzweil-Stieltjes sense.
References:
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