SINCE Namioka and Phelps, starting with Asplund’s pioneering work, introduced the no-tion of Asplund spaces (those are Banach spaces on which every continuous convex function isFrechet differentiable on a dense G_δ ...
Recently, some scholars such as Boccardo, Callout and Rakotoson, studied studied the second-order partial differential equation u=f, where f∈L^1(Ω) (non-reflexive), more generally f∈M(Ω), M(Ω)=[C_c(Ω)]', the to...
Based on Refs. [1—8], we discuss the following problem in this note.Let (Ω, A, P)be a complete probability space and X be a separable Banach space with the dual X~*.
In nonequilibrium statistical physics, the entropy production and the irreversibility (nondetailed balance) play very important roles. For the simple case of the Markov chains, it is shown that a stationary Markov cha...
In 1936, J. Clarkson introduced the uniformly convex Banach spaces (UC spaces) for the purpose of giving concrete examples of spaces possessing the Radon-Nikodym property for
The equilibrium problem of Green potentials for the Brownian motion has attracted general attention. The existence of equilibrium measure μ_B is proved, and the fundamental relation between the potential kernel u(x, ...