We present a complete characterization of the metric compactification of Lp spaces for 1≤p<∞. Each element of the metric compactification of Lp is represented by a random measure on a certain Polish space. By way of illustration, we revisit the Lp-mean ergodic theorem for 1<p<∞, and Alspach’s example of an isometry on a weakly compact convex subset of L1 with no fixed points.
- Mathematics - Functional Analysis
- Mathematics - Metric Geometry
- Mathematics - Probability