TY - JOUR
AU - O. M. Baranovskyi
AU - M. V. Pratsiovytyi
AU - H. M. Torbin
PY - 2007/09/25
Y2 - 2023/03/24
TI - Topological and metric properties of sets of real numbers with conditions on their expansions in Ostrogradskii series
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 59
IS - 9
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3379
AB - 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.
ER -