Uniformly distributed measure: Difference between revisions

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Line 4: :<math>\mathbf{B}_{r}(x) := \{ z \in X \| d(x, z) < r \}.</math> ==Christensen~~’~~'s lemma== As it turns out, uniformly distributed measures are very rigid objects. On any ~~“~~"decent~~”~~" metric space, the uniformly distributed measures form a one-parameter linearly dependent family: Let ''μ'' and ''ν'' be uniformly distributed Borel regular measures on a [[separable space\|separable]] metric space (''X'', ''d''). Then there is a constant ''c'' such that ''μ'' = ''cν''. Line 25: \| last = Mattila \| first = Pertti \| author-link = Pertti Mattila \| title = Geometry of sets and measures in Euclidean spaces: Fractals and rectifiability \| url = https://archive.org/details/geometryofsetsme0000matt \| url-access = registration \| series = Cambridge Studies in Advanced Mathematics No. 44 \| publisher = Cambridge University Press