It is shown that for each r 3, a random r-regular graph on 2n vertices is equivalent in a certain sense to a set of r randomly chosen disjoint perfect matchings of the 2n vertices, as n ! 1. This equivalence of two sequences of probabilistic spaces, called contiguity, occurs when all events almost sure in one sequence of spaces are almost sure in the other, and vice versa. The corresponding sta...

Given a sequence {Ek}k of almost-minimizing clusters in R which converges in L to a limit cluster E we prove the existence of C-diffeomorphisms fk between ∂E and ∂Ek which converge in C to the identity. Each of these boundaries is divided into C-surfaces of regular points, C-curves of points of type Y (where the boundary blows-up to three half-spaces meeting along a line at 120 degree) and isol...

We study Lipschitz differentiability spaces, a class of metric measure spaces introduced by Cheeger in [8]. We show that if an Ahlfors regular Lipschitz differentiability space has charts of maximal dimension, then, at almost every point, all its tangents are uniformly rectifiable. In particular, at almost every point, such a space admits a tangent that is isometric to a finite-dimensional Bana...

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 introduce the concepts of fuzzy (r, s)-regular open sets and fuzzy almost (r, s)-continuous mappings on the intuitionistic fuzzy topological spaces in Šostak’s sense. Also we investigate the equivalent conditions of the fuzzy almost (r, s)-continuity.