Funktionen von beschränkter Variatiou in der Theorie der Gleichverteilung

By E. Hlawka. 1961

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Determinantal Point Processes for Machine Learning (2012, methodology): “This deterministic uniformity property makes quasirandom sets useful for Monte Carlo estimation via (among other results) the Koksma-Hlawka inequality [Hlawka, 1961, Niederreiter , 1992].”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, unknown): “3 (Koksma-Hlawka inequality, see [68]).”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, background): “For example, a widely cited result is the Koksma-Hlawka theorem [191] (Koksma proved the onedimensional version [223]), which states that for any function with a variation in the sense of Hardy and Krause V (f) that is finite, we have the upper bound”
Walsh Spaces Containing Smooth Functions and Quasi-Monte Carlo Rules of Arbitrary High Order (2008, unknown): “In view of Corollary 3 and the explanation which followed it is hence not surprising that the classical examples and theory (see for example [6, 7, 17, 20, 23, 30, 42, 48]) only yielded a convergence of O(qm(−1+ε)) for any ε > 0 (the ε here is used to hide the powers of m).”
A Hilbert Space Embedding for Distributions (2007, background): “This can be answered by an extension of the KoksmaHlawka inequality [61].”