It is shown that if (Xn)n is a Bochner integrable stochastic process taking values in a Banach lattice E, the convergence of f(Xn) to f(X) where f is in a total subset of E∗ implies the a.s. convergence. For any Banach space E-valued stochastic process of Pettis integrable strongly measurable functions (Xn)n, the convergence of f(Xn) to f(X) for each f in a total subset of E∗ implies the conver...

This paper introduces a new model of environments with a large number of agents and stochastic characteristics. We consider sequences of finite but increasingly large economies that ‘discretize’ the continuum. In the limit we obtain a model that is continuum-like in important respects, yet it has a countable set of agents with a finitely additive, ‘uniform’ distribution. In this model, the law ...

We prove two existence theorems for the integrodifferential equation of mixed type: x′(t) = f (t,x(t), t0k1(t,s)g(s,x(s))ds, ∫ a 0k2(t,s)h(s,x(s))ds), x(0) = x0, where in the first part of this paper f , g, h, x are functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil (HK). In the second part f , g, h, x are weakly-weakly sequentially continuous fu...

In a recent paper the author proved that if Q is any compact metric space containing non-denumerably many points and C(Q) is the Banach space of all continuous functional over ft, then there is a Pettis integrable function from the unit interval to C(0) whose integral fails to be weakly differentiable on a set of positive measure. The purpose of this note is to obtain the same result, assuming ...