It is shown that the convergence of convolution products of probability measures on certain non-locally compact topological abelian groups can be verified by means of characteristic functionals. Analogous results are obtained also for almost everywhere convergence of series of independent random elements in the considered groups. A connection with the Sazonov property of the groups is discussed...

In this brief note, we prove that every space is a sequence-covering image of a topological sum of convergent sequences. As the application of this result, sequence-covering images of locally compact metric spaces (or, locally separable metric spaces, metric spaces) and sequentially-quotient images of a locally compact metric spaces (or, locally separable metric spaces, metric spaces) are equiv...

We study several questions involving relative Ricci-flat Kähler metrics for families of log Calabi-Yau manifolds. Our main result states that if $p:(X,B)\to Y$ is a fiber space such $(X\_y, B|{X\_y})$ generically klt, $K{X/Y}+B$ relatively trivial and $p\_\*(m(K\_{X/Y}+B))$ Hermitian flat some suitable integer $m$, then $p$ locally trivial. Motivated by in birational geometry, we investigate th...

The local behavior of mappings with the inverse Poletsky inequality between metric spaces is studied. case where one satisfies condition weak sphericalization, similar to Riemannian sphere (extended Euclidean space), and locally linearly connected under a mapping considered. It proved that equicontinuity corresponding families two domains, which domain weakly flat boundary, another fixed compac...

we classify the paracontact riemannian manifolds that their rieman-nian curvature satisfies in the certain condition and we show that thisclassification is hold for the special cases semi-symmetric and locally sym-metric spaces. finally we study paracontact riemannian manifolds satis-fying r(x, ξ).s = 0, where s is the ricci tensor.

In this paper we show how the solar system, galactic, and cosmological scales, are accommodated in a single framework, namely, derivative expansion framework. We construct locally inertial static metric, based on Einstein equations method, which describes Schwarzschild black hole immersed dark matter energy. The leading order metric corresponds to first galaxy, second cosmology. It is shown cap...

A Bochner flat Kähler manifold is a Kähler manifold with vanishing Bochner curvature tensor. We shall give a uniformization of Bochner flat Kähler manifolds. One of the aims of this paper is to give a correction to the proof of our previous paper [9] concerning uniformization of Bochner flat Kähler manifolds. A Bochner flat locally conformal Kähler manifold is a locally conformal Kähler manifol...