The purpose of this paper is to introduce the notion of weighted almost convergence of a sequence and prove that this sequence endowed with the sup-norm [Formula: see text] is a BK-space. We also define the notions of weighted almost conservative and regular matrices and obtain necessary and sufficient conditions for these matrix classes. Moreover, we define a weighted almost A-summable sequenc...

We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the author’s analytic approach, we generalize the so-called Fundamental Lemma giving independent process approximation in the total variation distance of the compone...

Let f denotes the space of almost convergent sequences, and f̂ also be the domain of the generalized di erence matrix B(r, s) in the sequence space f . The present paper is devoted to studing on the sequence spaces f̂ and f̂ s. Furthermore, the βand γ-duals of the space f̂ are determined. Finally, the classes (f̂ : μ) and (μ : f̂) of in nite matrices are characterized and the characterizations of som...

In this paper we investigate some new sequence spaces which naturally emerge from the concept of almost convergence. Just as ordinary, absolute and strong summability, it is expected that almost convergence must give rise to almost, absolutely almost and strongly almost summability. Almost and absolutely almost summable sequences have been discussed by several authors. The object of this paper ...

We answer positively a question of J. Rosenblatt (1988), proving the existence of a sequence (ci) with ∑∞ i=1 |ci| = ∞, such that for every dynamical system (X,Σ, m, T ) and f ∈ L1(X), ∑∞i=1 cif(T ix) converges almost everywhere. A similar result is obtained in the real variable context.

The classical summability methods of Borel (B) and Euler (E(λ), λ > 0) play an important role in many areas of mathematics. For instance, in summability theory they are perhaps the most important methods other than the Cesàro (Cα) and Abel (A) methods, and two chapters of the classic book of Hardy (1949) are devoted to them. In probability, the distinction between methods of Cesàro-Abel and Eul...

A population of players repeatedly plays an n strategy symmetric game. Players update their strategies by sampling the behavior of k opponents and playing a best response to the distribution of strategies in the sample. Suppose the game possesses a 1 k -dominant strategy which is initially played by a positive fraction of the population. Then if the population size is large enough, play converg...

{V : V ∈ Vn} = X . Clearly, every Menger space is almost Menger and every almost Menger space is weakly Menger, but the converses do not hold (see Examples 2.1 and 2.2). On the study of weakly Menger spaces, almost Menger spaces and Menger spaces, the readers can see the references [2, 3, 4, 5, 6]. Here we investigate the relationships among almost Menger spaces, weakly Menger spaces and Menger...

The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of...

Let $S$ be a semitopological semigroup. The $wap-$ compactification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the $Lmc-$ compactification of semigroup $S$ is a universal semigroup compactification of $S$, which are denoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internal construction of ...