# On strongly Pettis integrable functions in locally convex spaces.

N. D. Chakraborty; Sk. Jaker Ali

Revista Matemática de la Universidad Complutense de Madrid (1993)

- Volume: 6, Issue: 2, page 241-262
- ISSN: 1139-1138

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topChakraborty, 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 -

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