A convergence in Riesz spaces is given axiomatically. A Bochner-type integral for Riesz space-valued functions is introduced and some Vitali and Lebesgue dominated convergence theorems are proved. Some properties and examples are investigated. A.M.S. SUBJECT CLASSIFICATION (2000): 28B15.

There are several generalizations of the space L1(R) of Lebesgue integrable functions taking values in the real numbers R (and defined on the usual Lebesgue measure space (Ω,Σ, μ) on [0, 1] ) to a space of strongly-measurable “integrable” (suitably formulated) functions taking values in a Banach space X. The most common generalization is the space L1(X) of Bochner-Lebesgue integrable functions....

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

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...

Abstract The aim of this paper is to establish the boundedness commutator [ b , g ˙ r ] \left[b,{\dot{g}}_{r}] generated by Littlewood-Paley g -functions {\dot{g}}_{r} a...

In this article, we study the regularity criteria for the 3D NavierStokes equations involving derivatives of the partial components of the velocity. It is proved that if ∇he u belongs to Triebel-Lizorkin space, ∇u3 or u3 belongs to Morrey-Campanato space, then the solution remains smooth on [0, T ].