On metrization of the space Dα[0, ∞)
A complete metric on the function space Dα[0, ∞) , which is a subspace of the space Dα[0, ∞) of functions without discontinuities of the second kind, is constructed. This metric converts Dα[0, ∞) into a complete separable metric space. It is a modification of a metric on Dα[0, 1) introduced by Wood...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2001-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/34423 |
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| Summary: | A complete metric on the function space Dα[0, ∞) , which is a subspace of the space Dα[0, ∞) of functions without discontinuities of the second kind, is constructed. This metric converts Dα[0, ∞) into a complete separable metric space. It is a modification of a metric on Dα[0, 1) introduced by Woodroofe, and is stronger than the well-known metrics on Dα[0, ∞). Conditions for compactmess of the subsets of Dα[0, ∞) are given.
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| ISSN: | 0132-2818 2335-898X |