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Methods for measuring the weak value of non local variables are investigated. We analyze local (indirect) measurement methods for obtaining the weak values. We also describe some new (direct) methods (Non local weak measurements) for…

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…

Some recent attempts at measuring non local weak values via local measurements are discussed and shown to be less robust than standard weak measurements. A method for measuring some non local weak values via non local measurements (non…

Motivated by recent investigations of Sophie Grivaux and \'Etienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of locally bounded orbit for a continuous linear operator $T:X\longrightarrow X$…

We consider a class of non-locally compact groups on which one may define a left-invariant, finitely additive measure taking values in some finitely generated extension of the field $\mathbb{R}$ of real numbers. In particular, we recover…

In the second part of the paper we consider a convolution of probability measures on spaces of locally finite configurations (subsets of a phase space) as well as their connection with the convolution of the corresponding correlation…

We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples…

It is shown that any transverse invariant measure of a foliated space can be considered as a measure on the ambient space.

Several new invariants for Lie algebroids have been discovered recently. We give an overview of these invariants and establish several relationships between them.

There are a number of measures of direct and indirect effects in the literature. They are suitable in some cases and unsuitable in others. We describe a case where the existing measures are unsuitable and propose new suitable ones. We also…

We prove several identities relating three-variable Mahler measures to integrals of inverse trigonometric functions. After deriving closed forms for most of these integrals, we obtain ten explicit formulas for three-variable Mahler…

We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding…

In this paper, we study Markovian random iterations of maps on standard measurable spaces. We establish a one-to-one correspondence between stationary measures and a certain class of invariant measures of a Markovian random iteration,…

We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…

We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild…

In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…

We present local invariants of multi-partite pure or mixed states, which can be easily calculated and have a straight-forward physical meaning. As an application, we derive a new entanglement criterion for arbitrary mixed states of $n$…

We consider impulsive dynamical systems defined on compact metric spaces and their respective impulsive semiflows. We establish sufficient conditions for the existence of probability measures which are invariant by such impulsive semiflows.…

Exploiting the notion of measurement-induced nonlocality [Phys.Rev. Lett. 106, 120401 (2011)], we introduce a new measure to quantify the nonbilocal correlation. We establish a simple relation between the nonlocal and nonbilocal measures…

In this paper we study Green measures for certain classes of random time change Markov processes where the random time change are inverse subordinators. We show the existence of the Green measure for these processes under the condition of…