in this paper, using the tools involving measures of noncompactness and darbo fixed point theorem forcondensing operator, we study the existence of solutions for a large class of generalized nonlinear quadraticfunctional integral equations. also, we show that solutions of these integral equations are locally attractive.furthermore, we present an example to show the efficiency and usefulness of ...

An atomless probability space (Ω,A, P ) is said to have the saturation property for a probability measure μ on a product of Polish spaces X×Y if for every random element f of X whose law is margX(μ), there is a random element g of Y such that the law of (f, g) is μ. (Ω,A, P ) is said to be saturated if it has the saturation property for every such μ. We show each of a number of desirable proper...

Building on the Ramsey–de Finetti idea of event exchangeability, we derive a characterization of probabilistic sophistication without requiring any of the various versions of monotonicity, continuity, or comparative likelihood assumptions imposed by Savage (1954), Machina and Schmeidler (1992), and Grant (1995). Our characterization identifies a unique and finitely-additive subjective probabili...

This paper investigates the stability of optimal solution sets to stochastic programs with complete recourse, where the underlying probability measure is understood as a parameter varying in some space of probability measures.piro proved Lipschitz upper semicontinuity of the solution set mapping. Inspired by this result, we introduce a subgradient distance for probability distributions and esta...

In the paper, we consider the application of the theory of probability metrics in several areas in the field of finance. First, we argue that specially structured probability metrics can be used to quantify stochastic dominance relations. Second, the methods of the theory of probability metrics can be used to arrive at a general axiomatic treatment of dispersion measures and probability metrics...

Let Mφ denote the set of Borel probability measures invariant under a topological action φ on a compact metrizable space X. For a continuous function f : X → R, a measure μ ∈ Mφ is called f -maximizing if ∫ f dμ = sup{ ∫ f dm : m ∈Mφ}. It is shown that if μ is any ergodic measure in Mφ, then there exists a continuous function whose unique maximizing measure is μ. More generally, if E is a non-e...

In many applications of information theory, information measures the reduction of uncertainty that results from the knowledge that an event has occurred. Even so, an item of information learned need not be the occurrence of an event but, rather, the change in probability distribution associated with an ensemble of events. This paper examines the basic account of information, which focuses on ev...

1 Construction of measures 3 1.