Pettis-Type Spaces for a Bounded Family of Measures

Jump To References Section

Authors

  • N. D. Chakraborty
     Department of Mathematics, The University of Burdwan, Burdwan-713104 (W.B.) ,IN
  • M. Sahu
     Department of Mathematics, The University of Burdwan, Burdwan-713104 (W.B.) ,IN
  • B. Sen
     Department of Mathematics, The University of Burdwan, Burdwan-713104 (W.B.) ,IN

Keywords:

Lebesgue-Type Spaces, Pettis-Type Spaces, Vitali's Convergence Theorem, Lebesgue Dominated Convergence Theorem, Young's Function, Orlicz Spaces.

Abstract

Let (Ω,Σ,μ) be a probability space and let N⊂ca (Σ) be a bounded family of positive measures and X be a Banach space. Let P1(N,X) be the Pettis-type spaces with respect to N. Assuming that X is weakly sequentially complete, we prove the completeness of P1(N,X) with respect to the Pettis semi-norm. Also we prove the Vitali's convergence theorem, Lebesgue dominated theorem and a necessary and sufficient condition for a function to belong to P1(N,X).

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2003-12-01

How to Cite

Chakraborty, N. D., Sahu, M., & Sen, B. (2003). Pettis-Type Spaces for a Bounded Family of Measures. The Journal of the Indian Mathematical Society, 70(1-4), 111–119. Retrieved from http://informaticsjournals.com/index.php/jims/article/view/21914

Issue

Volume 70, Issue 1-4, January-December 2003

Section

Articles

License

Copyright (c) 2003 N. D. Chakraborty, M. Sahu, B. Sen

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.