On strongly Pettis integrable functions in locally convex spaces.

@article{Chakraborty1993,
abstract = {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 integrable by seminorm. For a bounded function another characterization has been given for the relative compactness of the range of the indefinite Pettis integral. Dunford-Pettis-Phillips theorem has been generalized to locally convex spaces and as a corollary of this theorem some results which are valid for Banach spaces have been extended to locally convex spaces.},
author = {Chakraborty, N. D., Jaker Ali, Sk.},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Espacios localmente convexos; Medidas del vector-estimación; Integrales de Pettis; relative compactness; range; indefinite Pettis integral; Dunford-Pettis- Phillips theorem; locally convex spaces; strongly Pettis integrable functions},
language = {eng},
number = {2},
pages = {241-262},
title = {On strongly Pettis integrable functions in locally convex spaces.},
url = {http://eudml.org/doc/43863},
volume = {6},
year = {1993},
}

TY - JOUR
AU - Chakraborty, N. D.
AU - Jaker Ali, Sk.
TI - On strongly Pettis integrable functions in locally convex spaces.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1993
VL - 6
IS - 2
SP - 241
EP - 262
AB - 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 integrable by seminorm. For a bounded function another characterization has been given for the relative compactness of the range of the indefinite Pettis integral. Dunford-Pettis-Phillips theorem has been generalized to locally convex spaces and as a corollary of this theorem some results which are valid for Banach spaces have been extended to locally convex spaces.
LA - eng
KW - Espacios localmente convexos; Medidas del vector-estimación; Integrales de Pettis; relative compactness; range; indefinite Pettis integral; Dunford-Pettis- Phillips theorem; locally convex spaces; strongly Pettis integrable functions
UR - http://eudml.org/doc/43863
ER -