Lattice-valued entropy functions defined by a lattice-valued possibilistic distribution π on a space Ω are defined as the expected value (in the sense of Sugeno integral) of the complement of the value π(ω) with ω ranging over Ω. The analysis is done in parallel for two alternative interpretations of the notion of complement in the complete lattice in question. Supposing that this complete latt...

The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued t...

Flexible boundary-condition methods couple an isolated defect to bulk through the bulk lattice Green's function. Direct computation of the lattice Green's function requires projecting out the singular subspace of uniform displacements and forces for the infinite lattice. We calculate the convergence rates for elastically isotropic and anisotropic cases for three different techniques: relative d...

where (n1,n2, . . . ,nd)= n∈ Z+. Recently, Thanh [11] proved (1.1) under condition of uniform integrability of {|Xn|p, n∈ Z+}. Mean convergence theorems for sums of random elements Banach-valued are studied by many authors. The reader may refer to Wei and Taylor [12], Adler et al. [2], Rosalsky and Sreehari [9], or more recently, Rosalsky et al. [10], Cabrera and Volodin [3]. However, we are un...

Measure spaces, measurable functions and positive measures, integration, convergence*. Examples. 1) fn(x) = n−1χ(0,n)(x), 2) fn(x) = χ(n,n+1)(x), 3) fn(x) = nχ[0,1/n](x), 4) L1 convergent but oscillating. Definition. pointwise convergence, uniform convergence, and convergence in Lp . Definition. We say that { fn} of measurable complex-valued functions on (X ,M ,μ) is Cauchy in measure if for ev...

The strong Whitney convergence on bornology introduced by Caserta in [9] is a generalization of the uniform Beer-Levi [5]. This paper aims to study some important topological properties space all real valued continuous functions metric endowed with topologies and bornology. More precisely, we investigate metrizability, various countability properties, countable tightness, Fr?chet property these...