Related papers: Bounded Scale Measure and Property A
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…
The main results of this paper show that various coarse (`large scale') geometric properties are closely related. In particular, we show that property A implies the operator norm localisation property, and thus that norms of operators…
A positive real interval, [a, b], can be partitioned into sub-intervals such that sub-interval widths divided by sub-interval "average" values remains constant. That both Arithmetic Mean and Geometric Mean "average" values produce constant…
With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…
Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an…
Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…
Let $(X, d)$ be a compact metric space and let $\mathcal{M}(X)$ denote the space of all finite signed Borel measures on $X$. Define $I \colon \mathcal{M}(X) \to \R$ by \[ I(\mu) = \int_X \int_X d(x,y) d\mu(x) d\mu(y), \] and set $M(X) =…
There are two primary goals to this paper. In the first part of the paper we study smooth metric measure spaces (M^n,g,e^{-f}dv_g) and give several ways of characterizing bounds -Kg\leq \Ric+\nabla^2f\leq Kg on the Ricci curvature of the…
Let $(X,d)$ be a compact metric space. We consider the behavior of probability measures $\mu$ with the property that $$ \int_{X} d(x, y) d\mu(y) \qquad \mbox{is independent of}~x \in X.$$ It appears that such measures, when they exist,…
Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data and with compositional data, like percentages and the like. If the natural measure of difference is not the absolute…
Recently, Taneja studied two one parameter generalizations of J-divergence, Jensen-Shannon divergence and Arithmetic-Geometric divergence. These two generalizations in particular contain measures like: Hellinger discrimination, symmetric…
We classify generalized Wallach spaces which are g.o. spaces. We also investigate homogeneous geodesics in generalized Wallach spaces for any given invariant Riemannian metric and we give some examples.
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
In this paper,\ the authors define a space with an uniform base at non-isolated points, give some characterizations of images of metric spaces by boundary-compact maps, and study certain relationship among spaces with special base…
A new refinement of the triangle inequality is presented in normed linear spaces. Moreover, a simple characterization of inner product spaces is obtained by using the skew-angular distance.
It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized…
We advance scale-invariance arguments for systems that are governed (or approximated) by a $q-$Gaussian distribution, i.e., a power law distribution with exponent $Q=1/(1-q); q \in \mathbb{R}$. The ensuing line of reasoning is then compared…
Separation bounds are a fundamental measure of the complexity of solving a zero-dimensional system as it measures how difficult it is to separate its zeroes. In the positive dimensional case, the notion of reach takes its place. In this…
Gauging is a general procedure for mapping a quantum many-body system with a global symmetry to one with a local gauge symmetry. We consider a generalized gauging map that does not enforce gauge symmetry at all lattice sites, and show that…
A concept of the generalized quantum measurement is introduced as the transformation, which establishes a correspondence between the initial states of the object system and final states of the object--measuring device (meter) system with…