A uniformly spread measure criterion

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چکیده

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M ay 2 00 8 A uniformly spread measure criterion

We prove that if all shifts of a measure in the Euclidean space are close in a sense to each other, then this measure is close to the Lebesgue one. Let (an)n∈N be a discrete sequence in R , i.e., a map N → R such that its image {an}n∈N has no limit point in R d and each x ∈ {an}n∈N has at most a finite multiplicity. Following Laczkovich [1], [2], we say that the sequence is uniformly spread ove...

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ژورنال

عنوان ژورنال: Analysis and Mathematical Physics

سال: 2011

ISSN: 1664-2368,1664-235X

DOI: 10.1007/s13324-011-0008-z