The following interesting structural theorem is proved: let {X n } be an arbitrary (not necessarily tight) sequence of real random variables (r.v.) with tail σ-field ; then, after a suitable enlargement of the basic probability space, one can find a subsequence {X n k } and a ...
Lacunary (R, p, M)-summabilityweighted mean methodsanalytic continuationuniversal approximationdensity propertiesIn this article summability methods of weighted mean type are considered which are generated by a lacunary sequence of positive minimal density. The interdependencies between the topological ...
Define lacunary. lacunary synonyms, lacunary pronunciation, lacunary translation, English dictionary definition of lacunary. n. pl. la·cu·nae or la·cu·nas 1. An empty space or a missing part; a gap: "self-centered in opinion, with curious lacunae of
For example, for the ascending sequence s n , n = 1, 2, 3, ..., generated by the ordered numbers of the form 2i3j, i, j = 1, 2, 3, ..., we prove that the set of real numbers α such that inf n∈ℕ n‖s n α‖ > 0 is a set of Hausdorff dimension 1. The ...
摘要: p/ pWe introduce new sequence space involving lacunary sequence connected with Cesaro sequence space and examine some geometric properties of this space equipped with Luxemburg norm./p关键词: cross-entropy method clustering vector quantization simulation global optimization ...
In 1975 Philipp proved the following law of the iterated logarithm (LIL) for the discrepancy of lacunary series: let (n k ) k ≥ 1 be a lacunary sequence of positive integers, i.e. a sequence satisfying the Hadamard gap condition n k+1/n k > q > Then 1/(4 Ö2) £ lim...
Lacunary sequenceThe sequence X = {Xk} of fuzzy numbers is statistically convergent to the fuzzy number X0 provided that for each ϵ ≺ 0limln{the number ofk⩽n:d(Xk,X0)⩾ϵ}=0. In this paper we study a related concept of convergence in which the set {k: k⩽n} is ...
The concepts of Wijsman asymptotically equivalence, Wijsman asymptotically statistically equivalence, Wijsman asymptotically lacunary equivalence and Wijsman asymptotically lacunary statistical equivalence for sequences of sets were studied by Ulusu and
This study examines the lacunary statistical convergence of sequences of soft points in soft topological spaces, employing a density defined by an unbounded modulus function. Basic results and inclusion theorems concerning this convergence are presented.Springer Berlin HeidelbergSoft ComputingBayram, Erdal...
Let (t n ) be a sequence of positive numbers and ε>0N 0 n≥N 0 :t n+1 t n ≥1+1 n ε· Then for every number δ>0 the set A δ =x∈|c(x)>0n∈∥t n x∥>c(x) n δ is an α-winning set if a given number α belongs to (0,1/2), i.e. windimA δ =1/...