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Erschienen in:
2013 | OriginalPaper | Buchkapitel
6. Quantitative Relationships Between Minimal Distances and Minimal Norms
verfasst von : Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi
Erschienen in: The Methods of Distances in the Theory of Probability and Statistics
Verlag: Springer New York
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Abstract
The goals of this chapter are to: Explore the conditions under which there is equality between the Kantorovich and the Kantorovich–Rubinstein functionals; Provide inequalities between the Kantorovich and Kantorovich–Rubinstein functionals; Provide criteria for convergence, compactness, and completeness of probability measures in probability spaces involving the Kantorovich and Kantorovich–Rubinstein functionals; Analyze the problem of uniformity between the two functionals.