Displaying similar documents to “A note on Olech's Lemma”

From weak to strong types of L E 1 -convergence by the Bocce criterion

Erik Balder, Maria Girardi, Vincent Jalby (1994)

Studia Mathematica

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Necessary and sufficient oscillation conditions are given for a weakly convergent sequence (resp. relatively weakly compact set) in the Bochner-Lebesgue space ℒ E 1 to be norm convergent (resp. relatively norm compact), thus extending the known results for ℒ ℝ 1 . Similarly, necessary and sufficient oscillation conditions are given to pass from weak to limited (and also to Pettis-norm) convergence in ℒ E 1 . It is shown that tightness is a necessary and sufficient condition to pass from limited to...

Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces

Riccarda Rossi, Giuseppe Savaré (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Compactness in the space L p ( 0 , T ; B ) , B being a separable Banach space, has been deeply investigated by J.P. Aubin (1963), J.L. Lions (1961, 1969), J. Simon (1987), and, more recently, by J.M. Rakotoson and R. Temam (2001), who have provided various criteria for relative compactness, which turn out to be crucial tools in the existence proof of solutions to several abstract time dependent problems related to evolutionary PDEs. In the present paper, the problem is examined in view of Young measure...

Pointwise compactness and continuity of the integral.

G. Vera (1996)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we bring together the different known ways of establishing the continuity of the integral over a uniformly integrable set of functions endowed with the topology of pointwise convergence. We use these techniques to study Pettis integrability, as well as compactness in C(K) spaces endowed with the topology of pointwise convergence on a dense subset D in K.

On strongly Pettis integrable functions in locally convex spaces.

N. D. Chakraborty, Sk. Jaker Ali (1993)

Revista Matemática de la Universidad Complutense de Madrid

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Some characterizations have been given for the relative compactness of the range of the indefinite Pettis integral of a function on a complete finite measure space with values in a quasicomplete Hausdorff locally convex space. It has been shown that the indefinite Pettis integral has a relatively compact range if the functions is measurable by seminorm. Separation property has been defined for a scalarly measurable function and it has been proved that a function with this property is...