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POINT DISTRIBUTIONS IN COMPACT METRIC SPACES
Author(s) -
Skriganov M. M.
Publication year - 2017
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579317000286
Subject(s) - mathematics , metric space , injective metric space , invariant (physics) , convex metric space , metric (unit) , intrinsic metric , pure mathematics , uniform continuity , metric map , mathematical analysis , discrete mathematics , operations management , economics , mathematical physics
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).