Topological and metric properties of sets of real numbers with conditions on their expansions in Ostrogradskii series

  • O. M. Baranovskyi
  • M. V. Pratsiovytyi
  • H. M. Torbin


We study topological and metric properties of the set $$C\left[\overline{O}^1, \{V_n\}\right] = \left\{x:\; x= ∑_n \frac{(−1)^{n−1}}{g_1(g_1 + g_2)…(g_1 + g_2 + … + g_n)},\quad g_k ∈ V_k ⊂ \mathbb{N}\right\}$$ with certain conditions on the sequence of sets $\{V_n\}$. In particular, we establish conditions under which the Lebesgue measure of this set is (a) zero and (b) positive. We compare the results obtained with the corresponding results for continued fractions and discuss their possible applications to probability theory.
How to Cite
Baranovskyi, O. M., M. V. Pratsiovytyi, and H. M. Torbin. “Topological and Metric Properties of Sets of Real Numbers With Conditions on Their Expansions in Ostrogradskii Series”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, no. 9, Sept. 2007, pp. 1155–1168,
Research articles