Abstract: Suppose $${\Lambda}$$ is a discrete infinite set of nonnegative real numbers. We say that $${\Lambda}$$ is type 1 if the series $$s(x)=\sum\nolimits_{\lambda\in\Lambda}f(x+\lambda)$$ satisfies a “zero-one” law. This means that for any non-negative measurable $$f \colon \mathbb{R} \to [0,+ {\infty})$$ either the convergence set $$C(f, {\Lambda})=\{x: s(x)<+ {\infty} \}= \mathbb{R}$$ modulo sets of Lebesgue zero, or its complement the divergence set $$D(f, {\Lambda})=\{x: s(x)=+ {\infty} \}= \mathbb{R}$$ modulo sets of measure zero. If $${\La...
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Topics: 
Combinatorics
Discrete mathematics