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.
@article{urn:eudml:doc:43863,
title = {On strongly Pettis integrable functions in locally convex spaces.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {6},
year = {1993},
pages = {241-262},
zbl = {0815.28006},
mrnumber = {MR1269755},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:43863}
}
Chakraborty, N. D.; Jaker Ali, Sk. On strongly Pettis integrable functions in locally convex spaces.. Revista Matemática de la Universidad Complutense de Madrid, Tome 6 (1993) pp. 241-262. http://gdmltest.u-ga.fr/item/urn:eudml:doc:43863/