02579nam a22003975a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001600185084003600201100003000237245014700267260008200414300003400496336002600530337002600556338003600582347002400618490008300642506006600725520105000791650004701841650003701888650003101925650003301956650004101989650005302030856003202083856006602115199-151214CH-001817-320151214234500.0a fot ||| 0|cr nn mmmmamaa151214e20160105sz fot ||| 0|eng d a978303719658870a10.4171/1582doi ach0018173 7aPBMP2bicssc 7aPBT2bicssc a53-xxa28-xxa30-xxa60-xx2msc1 aShioya, Takashi,eauthor.10aMetric Measure Geometryh[electronic resource] :bGromov’s Theory of Convergence and Concentration of Metrics and Measures /cTakashi Shioya3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2016 a1 online resource (194 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v251 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book studies a new theory of metric geometry on metric measure spaces, originally developed by M. Gromov in his book “Metric Structures for Riemannian and Non-Riemannian Spaces” and based on the idea of the concentration of measure phenomenon due to Lévy and Milman. A central theme in this text is the study of the observable distance between metric measure spaces, defined by the difference between 1-Lipschitz functions on one space and those on the other. The topology on the set of metric measure spaces induced by the observable distance function is weaker than the measured Gromov–Hausdorff topology and allows to investigate a sequence of Riemannian manifolds with unbounded dimensions. One of the main parts of this presentation is the discussion of a natural compactification of the completion of the space of metric measure spaces. The stability of the curvature-dimension condition is also discussed.
This book makes advanced material accessible to researchers and graduate students interested in metric measure spaces.07aDifferential & Riemannian geometry2bicssc07aProbability & statistics2bicssc07aDifferential geometry2msc07aMeasure and integration2msc07aFunctions of a complex variable2msc07aProbability theory and stochastic processes2msc40uhttps://doi.org/10.4171/158423cover imageuhttps://www.ems-ph.org/img/books/shioya_mini.jpg