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- Title
Isometries of Spaces of Radon Measures.
- Authors
Wójtowicz, Marek
- Abstract
Let Ω and I denote a compact metrizable space with card(Ω)≥2 and the unit interval, respectively. We prove Milutin and Cantor-Bernstein type theorems for the spaces M(Ω) of Radon measures on compact Hausdorff spaces Ω. In particular, we obtain the following results: (1) for every infinite closed subset K of βN the spaces M(K), M(βN), and M(Ω2ℵ0) are order-isometric; (2) for every discrete space Γ with m≔card(Γ)>ℵ0 the spaces M(βΓ) and M(I2m) are order-isometric, whereas there is no linear homeomorphic injection from C(βT) into C(I2m).
- Subjects
RADON measures; HAUSDORFF spaces; RIESZ spaces; BANACH spaces; BANACH lattices
- Publication
Journal of Function Spaces, 2017, p1
- ISSN
2314-8896
- Publication type
Article
- DOI
10.1155/2017/3850817