Metric Measure Geometry

Gromov’s Theory of Convergence and Concentration of Metrics and Measures

  • Takashi Shioya

    Tohoku University, Sendai, Japan
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FrontmatterDownload pp. i–iv
ContentsDownload pp. v–vi
IntroductionDownload pp. vii–xi
1Preliminaries from measure theorypp. 1–8
2The Lévy–Milman concentration phenomenonpp. 9–27
3Gromov–Hausdorff distance and distance matrixpp. 29–33
4Box distancepp. 35–63
5Observable distance and measurementpp. 65–88
6The space of pyramidspp. 89–101
7Asymptotic concentrationpp. 103–125
8Dissipationpp. 127–136
9Curvature and concentrationpp. 137–174
Bibliographypp. 175–178
Indexpp. 179–182