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Integral Probability Metrics and Their Generating Classes of Functions
- Part of
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- Journal:
- Advances in Applied Probability / Volume 29 / Issue 2 / June 1997
- Published online by Cambridge University Press:
- 01 July 2016, pp. 429-443
- Print publication:
- June 1997
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- Article
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We consider probability metrics of the following type: for a class
of functions and probability measures P, Q we define 
A unified study of such integral probability metrics is given. We characterize the maximal class of functions that generates such a metric. Further, we show how some interesting properties of these probability metrics arise directly from conditions on the generating class of functions. The results are illustrated by several examples, including the Kolmogorov metric, the Dudley metric and the stop-loss metric.
of functions and probability measures 
A unified study of such 