On convergence determining and separating classes of functions |
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Authors: | Douglas Blount Michael A. Kouritzin |
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Affiliation: | 1. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, USA;2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada |
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Abstract: | Herein, we generalize and extend some standard results on the separation and convergence of probability measures. We use homeomorphism-based methods and work on incomplete metric spaces, Skorokhod spaces, Lusin spaces or general topological spaces. Our contributions are twofold: we dramatically simplify the proofs of several basic results in weak convergence theory and, concurrently, extend these results to apply more immediately in a number of settings, including on Lusin spaces. |
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Keywords: | primary, 60B10 secondary, 60B05 |
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