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Cantorvals and incomplete sums of positive series

Building: Mykhailo Drahomanov National Pedagogical University

Room: Room C

Date: 2018-09-25 03:00 PM – 15:30

Last modified: 2018-09-24

#### Abstract

We present the construction of a continual family of positive series, the set of incomplete sums of which is Cantorval. Each series of this family has a property$$\sum\limits_{n=1}^{\infty}a_{n}=1,~~~\overline{\lim_{n\rightarrow\infty}}\frac{a_n}{\sum_{k=1}^{\infty}a_{n+k}}=+\infty.$$Moreover for any $\varepsilon>0$ there exists a series in this family, the Lebesgue measure of an incomplete sums set of which is greater than $ 1- \varepsilon $.