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arXiv · 1903.02502

Characterizing the metric compactification of $L_{p}$ spaces by random measures

Armando W. Gutiérrez
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Abstract

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.

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BibTeXRIS

Armando W. Gutiérrez. 2019-03-06. Characterizing the metric compactification of $L_{p}$ spaces by random measures. https://doi.org/10.1007/s43034-019-00024-1

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