Characterizing the metric compactification of $L_{p}$ spaces by random measures
19 Jun 2019
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Gutiérrez Armando W.
We present a complete characterization of the metric compactification of
$L_{p}$ spaces for $1\leq p < \infty$. Each element of the metric
compactification of $L_{p}$ is represented by a random measure on a certain
Polish space...By way of illustration, we revisit the $L_{p}$-mean ergodic
theorem for $1 < p < \infty$, and Alspach's example of an isometry on a weakly
compact convex subset of $L_{1}$ with no fixed points.(read more)