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A generalized moment problem in vector lattices. (English) Zbl 1006.28011
A moment problem is presented in the context of vector lattices. Let $$Y$$ be a (Dedekind) complete vector lattice and $$y_n$$ a sequence of elements in $$Y$$. There is given a necessary and sufficient condition in order that there exists a function $$g(t):[0,1] \to Y$$ of order bounded variation such that $\int _0^1t^ndg(t)=y_n, \qquad n=0,1,\dots\;.$
##### MSC:
 28B15 Set functions, measures and integrals with values in ordered spaces 47B65 Positive linear operators and order-bounded operators
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