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- W3023898103 abstract "From mostly a measure-theoretic consideration, we show that for every nonnegative, finite, and $L^{1}$ function on a given finite measure space there is some nontrivial sequence of real numbers such that the series, obtained from summing over the term-by-term products of the reals and the summands of any divergent series with positive, vanishing summands such as the harmonic series, is convergent and no greater than the integral of the function. In terms of inequalities, the implications add additional information on mathematical expectation and the behavior of divergent series with positive, vanishing summands, and establish in a broad sense some new, unexpected connections between probability theory and, for instance, number theory." @default.
- W3023898103 created "2020-05-13" @default.
- W3023898103 creator A5029548181 @default.
- W3023898103 date "2020-04-27" @default.
- W3023898103 modified "2023-10-14" @default.
- W3023898103 title "Tail Probability and Divergent Series" @default.
- W3023898103 doi "https://doi.org/10.48550/arxiv.2004.13541" @default.
- W3023898103 hasPublicationYear "2020" @default.
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