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- W2468074596 abstract "In the last chapter we extended the Markov–Kakutani Theorem—originally proved only for commuting families of continuous affine maps—to “solvable” families of such maps. We used our enhanced theorem to show that every solvable group is amenable and that Haar measure exists for every topological group that is both solvable and compact. By contrast, we’ve seen (Chap. 11) that the group(mathcal{R}) of origin-centric rotations of(mathbb{R}^{3}) is paradoxical, hence not amenable, and therefore not solvable. Now(mathcal{R}) is naturally isomorphic to the group(mathrm{SO(3)}) of 3 × 3 orthogonal real matrices with determinant 1 (Appendix D), a group easily seen to be compact. Thus not every compact group is amenable." @default.
- W2468074596 created "2016-07-22" @default.
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- W2468074596 date "2016-01-01" @default.
- W2468074596 modified "2023-09-27" @default.
- W2468074596 title "Beyond Markov–Kakutani" @default.
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- W2468074596 doi "https://doi.org/10.1007/978-3-319-27978-7_13" @default.
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