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- W1497237148 abstract "For every nonempty compact convex subset $K$ of a normed linear space a (unique) point $c_K in K$, called the generalized Chebyshev center, is distinguished. It is shown that $c_K$ is a common fixed point for the isometry group of the metric space $K$. With use of the generalized Chebyshev centers, the central measure $mu_X$ of an arbitrary compact metric space $X$ is defined. For a large class of compact metric spaces, including the interval $[0,1]$ and all compact metric groups, another `central' measure is distinguished, which turns out to coincide with the Lebesgue measure and the Haar one for the interval and a compact metric group, respectively. An idea of distinguishing infinitely many points forming a dense subset of an arbitrary compact metric space is also presented." @default.
- W1497237148 created "2016-06-24" @default.
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- W1497237148 date "2011-05-28" @default.
- W1497237148 modified "2023-09-27" @default.
- W1497237148 title "Central points and measures and dense subsets of compact metric spaces" @default.
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