Savchenko I. The Fractal Analysis of the Sets of Subsums of Numerical Series

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0416U004006

Thesis Registration Form

0416U004006.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

06-09-2016

Specialized Academic Board

Д 26.206.01

The Institute of Mathematics of NASU

Essay

The dissertation is devoted to topological, metric and fractal properties of the sets of subsums of numerical series. We study some classes of series such that sets of their subsums are perfect and either nowhere dense sets of zero (positive) Lebesgue measure or unions of nowhere dense set and in?nite union of intervals. Hausdor?-Besicovitch dimension of the set of subsums of the series is found if its Lebesgue measure is equal to zero.

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Files

aref.pdf

dis.pdf

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