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On series of translates of positive functions II

Authors
Journal
Indagationes Mathematicae
0019-3577
Publisher
Elsevier
Publication Date
Volume
12
Issue
3
Identifiers
DOI: 10.1016/s0019-3577(01)80013-6

Abstract

Abstract In this paper we continue our investigation of series of the form ∑ λ ∈ Λ ƒ(x + λ) . Given a sequence of natural numbers n 1 < n 2 < … we are interested in sets Λ of the form where 0 < α < 1. In case α = 1 q , where q > 1 is an integer, there is a zero-one law showing that for every measurable the above sum either converges almost everywhere or diverges almost everywhere. However, for any other value of α ∈ (0, 1) there is no such zero-one law.

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