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Weak Baire measurability of the balls in a Banach space

José Rodríguez (2008)

Studia Mathematica

Let X be a Banach space. The property (∗) “the unit ball of X belongs to Baire(X, weak)” holds whenever the unit ball of X* is weak*-separable; on the other hand, it is also known that the validity of (∗) ensures that X* is weak*-separable. In this paper we use suitable renormings of $ℓ^{\infty} (ℕ)$ and the Johnson-Lindenstrauss spaces to show that (∗) lies strictly between the weak*-separability of X* and that of its unit ball. As an application, we provide a negative answer to a question raised by K. Musiał....

Weak compactness criteria for set valued integrals and Radon Nikodym Theorem for vector valued multimeasures

Diomedes Bárcenas (2001)

Czechoslovak Mathematical Journal

Some criteria for weak compactness of set valued integrals are given. Also we show some applications to the study of multimeasures on Banach spaces with the Radon-Nikodym property.

Weak Convergence of Vector Measures on F-Space.

Tsang-hai Kuo (1975)

Mathematische Zeitschrift

Weak Fubini theorems for the Dobrakov integral

Charles W. Swartz (1980)

Czechoslovak Mathematical Journal

Weak integrals defined on Euclidean n-space

James Brooks, Jan Mikusiński (1972)

Studia Mathematica

Weak solutions of differential equations in Banach spaces

Mieczysław Cichoń (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we prove a theorem for the existence of pseudo-solutions to the Cauchy problem, x' = f(t,x), x(0) = x₀ in Banach spaces. The function f will be assumed Pettis-integrable, but this assumption is not sufficient for the existence of solutions. We impose a weak compactness type condition expressed in terms of measures of weak noncompactness. We show that under some additionally assumptions our solutions are, in fact, weak solutions or even strong solutions. Thus, our theorem is an essential...