A note on faces of convex sets
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917175767334912 |
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| author | Weis, Stephan |
| author_facet | Weis, Stephan |
| contents | The faces of a convex set owe their relevance to an interplay between convexity and topology that is systematically studied in the work of Rockafellar. Infinite-dimensional convex sets are excluded from this theory as their relative interiors may be empty. Shirokov and the present author answered this issue by proving that every point in a convex set lies in the relative algebraic interior of the face it generates. This theorem is proved here in a simpler way, connecting ideas scattered throughout the literature. This article summarizes and develops methods for faces and their relative algebraic interiors and applies them to spaces of probability measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00832 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on faces of convex sets Weis, Stephan Metric Geometry Probability 52A05, 46E27 The faces of a convex set owe their relevance to an interplay between convexity and topology that is systematically studied in the work of Rockafellar. Infinite-dimensional convex sets are excluded from this theory as their relative interiors may be empty. Shirokov and the present author answered this issue by proving that every point in a convex set lies in the relative algebraic interior of the face it generates. This theorem is proved here in a simpler way, connecting ideas scattered throughout the literature. This article summarizes and develops methods for faces and their relative algebraic interiors and applies them to spaces of probability measures. |
| title | A note on faces of convex sets |
| topic | Metric Geometry Probability 52A05, 46E27 |
| url | https://arxiv.org/abs/2404.00832 |