Open Access
2009 Continuity of a certain invariant of a measure on a CAT(0) space
Tetsu Toyoda
Nihonkai Math. J. 20(2): 85-97 (2009).


For a finitely supported probability measure $\mu$ on a complete CAT(0) space $Y$ , Izeki and Nayatani defined an invariant $\delta(\mu) \in [0,1]$ in [1]. The supremum of those for all such measures on $Y$ is an invariant of $Y$ , called the Izeki-Nayatani invariant, which plays an important role in the study of fixed-point property of groups. In this paper, we establish continuity of $\delta$ on the space of finitely supported probability measures. We prove the lower-semicontinuity of $\delta$ with respect to the $(L^2-)$ Wasserstein metric, and continuity with respect to some metric which induces a stronger topology.


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Tetsu Toyoda. "Continuity of a certain invariant of a measure on a CAT(0) space." Nihonkai Math. J. 20 (2) 85 - 97, 2009.


Published: 2009
First available in Project Euclid: 26 March 2010

zbMATH: 1201.53043
MathSciNet: MR2650461

Primary: 51F99

Keywords: CAT(0) space , Izeki-Nayatani invariant , Wasserstein distance

Rights: Copyright © 2009 Niigata University, Department of Mathematics

Vol.20 • No. 2 • 2009
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