We introduce the notion of type-symmetric randomized equilibrium (TSRE) by requiring those agents with the same type of characteristics to choose the same randomized choice. Such a notion provides a generic micro-foundation for the macro notion of equilibrium distribution, as used in the literature on games and economies with many agents. In particular, we show that if the space of agents is mo...

In this work, we present a bilinear Tb theorem for singular integral operators of Calderón-Zygmund type. We prove some new accretive type Littlewood-Paley results and construct a bilinear paraproduct for a para-accretive function setting. As an application of our bilinear Tb theorem, we prove product Lebesgue space bounds for bilinear Riesz transforms defined on Lipschitz curves.

Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.

We shall start by giving the definition of the entropy of dynamical system. Consider dynamical systems with discrete time. The phase space of dynamical system is denoted by M . It is equipped with σ-algebra M and a probability measure μ defined on M. In the general ergodic theory dynamics is given by a measurable transformation T of M onto itself preserving the measure μ. It is enough for many ...

in this paper boundedness and compactness of generalized composition oper-ators from logarithmic bloch type spaces to q_k type spaces are investigated.

In this paper we study the existence of solution of a nonlinear integral equation of (mixed type) Volterra-Fredholm type. As an application we prove the existence of solution of an initial value problem of fractional order in the space of Lebesgue integrable functions on the interval [0, 1]. 200 Mathematics Subject Classification: 26A33, 45J05, 39B05, 34A60, 34G20, 34K05.

We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko’s framework for polynomial space computability in Rn to define weakly pspace-random points, a new variant of polynomial space randomness. We show that the Lebesgue differentiation theorem holds for every weakly pspace-random point.

We show how to provide a structure of probability space to the set of execution traces on a nonconfluent abstract rewrite system, by defining a variant of a Lebesgue measure on the space of traces. Then, we show how to use this probability space to transform a non-deterministic calculus into a probabilistic one. We use as example λ+, a recently introduced calculus defined through type isomorphi...

We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko’s framework for polynomial space computability in R to define weakly pspace-random points, a new variant of polynomial space randomness. We show that the Lebesgue differentiation theorem characterizes weakly pspace random points. That is, a po...