Title: POINT DISTRIBUTIONS IN COMPACT METRIC SPACES
Abstract: MathematikaVolume 63, Issue 3 p. 1152-1171 Research Article POINT DISTRIBUTIONS IN COMPACT METRIC SPACES M. M. Skriganov, Corresponding Author M. M. Skriganov [email protected] St. Petersburg Department, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg, 191023 RussiaSearch for more papers by this author M. M. Skriganov, Corresponding Author M. M. Skriganov [email protected] St. Petersburg Department, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg, 191023 RussiaSearch for more papers by this author First published: 29 November 2017 https://doi.org/10.1112/S0025579317000286Citations: 7 Dedicated to the memory of Klaus Roth Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract We consider finite point subsets (distributions) in compact metric spaces. In the case of general rectifiable metric spaces, non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in metric balls are given (Theorem 1.1). We generalize Stolarsky's invariance principle to distance-invariant spaces (Theorem 2.1). For arbitrary metric spaces, we prove a probabilistic invariance principle (Theorem 3.1). Furthermore, we construct equal-measure partitions of general rectifiable compact metric spaces into parts of small average diameter (Theorem 4.1). Citing Literature Volume63, Issue32017Pages 1152-1171 RelatedInformation