On strongly Pettis integrable functions in locally convex spaces.

Chakraborty, N. D., and Jaker Ali, Sk.. "On strongly Pettis integrable functions in locally convex spaces.." Revista Matemática de la Universidad Complutense de Madrid 6.2 (1993): 241-262. <http://eudml.org/doc/43863>.

@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 -