Related papers: Approximations of expectations under infinite prod…
With any convex function F on a finite-dimensional linear space X such that F goes to infinity at infinity, we associate a Borel measure on the dual space X*. This measure is obtained by pushing forward the measure exp(-F(x))dx under the…
We consider the problem of finding the infimum, over probability measures being in a ball defined by Wasserstein distance, of the expected value of a bounded Lipschitz random variable on $\mathbf{R}^d$. We show that if the $\sigma-$algebra…
We consider a discrete-time Markov decision process with Borel state and action spaces. The performance criterion is to maximize a total expected {utility determined by unbounded return function. It is shown the existence of optimal…
In this paper, we study the conjunction of possibility measures when they are interpreted as coherent upper probabilities, that is, as upper bounds for some set of probability measures. We identify conditions under which the minimum of two…
We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an internal probability measure and its push-down measure is…
Weak values and measurements have been proposed as means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur…
In [12] we formulated an evolutionary game theory model as a dynamical system on the state space of finite signed Borel measures under the weak* topology. The focus of this paper is to extend the analysis to include the long-time behavior…
The second part of the paper mainly deals with convergence of infinite determinantal measures, understood as the convergence of the approximating finite determinantal measures. In addition to the usual weak topology on the space of…
A Banach space has the Schur property when every weakly convergent sequence converges in norm. We prove a Schur-like property for measures: if a sequence of finite signed Borel measures on a Polish space is such that it is bounded in total…
The aim of this paper is to investigate extremum problems with pay-off being the total variational distance metric defined on the space of probability measures, subject to linear functional constraints on the space of probability measures,…
In this article, we introduce a formal definition of the concept of probability tree and conduct a detailed and comprehensive study of its fundamental structural properties. In particular, we define what we term an inductive probability…
A game has approximate equilibria if for every $\epsilon >0$ there is an $\epsilon$-equilibrium. We show that there is a stochastic game that lacks approximate equilibria. This game has finitely many players and actions, their payoffs are…
On spaces of finite signed Borel measures on a metric space one has introduced the Fortet-Mourier and Dudley norms, by embedding the measures into the dual space of the Banach space of bounded Lipschitz functions, equipped with different --…
We consider positively supported Borel measures for which all moments exist. On the set of compactly supported measures in this class a partial order is defined via eventual dominance of the moment sequences. Special classes are identified…
We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when…
A strong mode of a probability measure on a normed space $X$ can be defined as a point $u$ such that the mass of the ball centred at $u$ uniformly dominates the mass of all other balls in the small-radius limit. Helin and Burger weakened…
We characterize a value of an observable by a `sum rule' for generally non-commuting observables and a `product rule' when restricted to a maximal commuting subalgebra of observables together with the requirement that the value is unity for…
This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative…
Weak measurement of a quantum system followed by postselection based on a subsequent strong measurement gives rise to a quantity called the weak value: a complex number for which the interpretation has long been debated. We analyse the…
Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement.…