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Concentration function for pyramid and quantum metric measure space


Author: Ryunosuke Ozawa
Journal: Proc. Amer. Math. Soc. 145 (2017), 1301-1315
MSC (2010): Primary 53C23, 28Axx
DOI: https://doi.org/10.1090/proc/13282
Published electronically: November 21, 2016
MathSciNet review: 3589327
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Abstract: In this paper, we generalize the concentration function for metric measure space to one for pyramid and quantum metric measure space. We also study the limit of the concentration function for convergent sequences of pyramids and quantum metric measure spaces.


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Additional Information

Ryunosuke Ozawa
Affiliation: Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
Email: ozawa@mpim-bonn.mpg.de

DOI: https://doi.org/10.1090/proc/13282
Keywords: Metric measure space, concentration function, observable distance, box distance, pyramid, quantum metric measure space
Received by editor(s): October 17, 2015
Received by editor(s) in revised form: May 5, 2016
Published electronically: November 21, 2016
Additional Notes: This work was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists (Grant Number 13J02664).
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2016 American Mathematical Society