Related papers: Tangent measures of non-doubling measures

Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…

For integers $a$ and $b\geq 2$, let $T_a$ and $T_b$ be multiplication by $a$ and $b$ on $\mathbb{T}=\mathbb{R}/\mathbb{Z}$. The action on $\mathbb{T}$ by $T_a$ and $T_b$ is called $\times a,\times b$ action and it is known that, if $a$ and…

We compare the entanglement of formation with a measure defined as the modulus of the negative eigenvalue of the partial transpose. In particular, we investigate whether both measures give the same ordering of density operators with respect…

We present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We…

We define a negative entanglement measure for separable states which shows that how much entanglement one should compensate the unentangled state at least for changing it into an entangled state. For two-qubit systems and some special…

We show the existence of a non-null locally finite measure on $l^{\infty}$ which is invariant by translations.

We study the randomness properties of reals with respect to arbitrary probability measures on Cantor space. We show that every non-computable real is non-trivially random with respect to some measure. The probability measures constructed in…

In this paper, we introduce the notion of a $\gamma$-density point for Lebesgue-measurable subsets of $\mathbb{R}$, where $\gamma$ is a modulus function, and study its basic measure-theoretic properties. We show that every $\gamma$-density…

We propose the following way of constructing quantum measure in Regge calculus: the full discrete Regge manifold is made continuous in some direction by tending corresponding dimensions of simplices to zero, then functional integral measure…

For function of one variable, differentiability is equivalent to the existence of tangent line as the limit of secant line. The genuine counterpart of this equivalence for function of several variables is obtained for the first time.

We have developed Bayesian formalism to describe the process of continuous measurement of entangled qubits. We start with the case of two qubits and then generalize it to an arbitrary number of qubits.

We study measures on the configuration spaces of two type particles. Gibbs measures on the such spaces are described. Main properties of corresponding relative energies densities and correlation functions are considered. In particular, we…

We consider skew products over subshifts of finite type in which the fibers are copies of the real line, and we study their mixing properties with respect to any infinite invariant measure given by the product of a Gibbs measure on the base…

This paper has two goals. The first is to present the construction, due to the author, of measures on non-archimedean analytic varieties associated to metrized line bundles and some of its applications. We take this opportunity to add…

For a nontrivial measurable set on the real line, there are always exceptional points, where the lower and upper densities of the set are neither zero nor one. We quantify this statement, following work by V. Kolyada, and obtain the…

A positive non-commutative (NC) measure is a positive linear functional on the free disk operator system which is generated by a $d$-tuple of non-commuting isometries. By introducing the hybrid forms, their Cauchy transforms, and techniques…

The three-tangle is a measure of three-way entanglement in a system of three qubits. For a pure state, it can be understood as the residual entanglement not accounted for by pairwise entanglements between individual qubits. Here we define…

We study the pointwise dimension for a new class of projection measures on arbitrary fractal limit sets without separation conditions. We prove that the pointwise dimension exists a.e. for this class of measures associated to equilibrium…

We give two versions of the natural extension of a specific greedy beta-transformation with deleted digits. We use the natural extension to obtain an explicit expression for the invariant measure, equivalent to the Lebesgue measure, of this…

A path independent measure in order parameter space is introduced such that, when integrated along any closed contour in a three dimensional nematic phase, it yields the topological charge of any line defects encircled by the contour. A…