Weak Integration of Vector-Valued Functions

Jump To References Section

Authors

  • Surjit Singh Khurana
     Department of Mathematics, 101 MacLean Hall, The University of Iowa, Iowa City, Iowa 52240 ,US

Abstract

In this paper, X is a Hausdorff topological space, (μ a finite, positive, and countably additive set function on a σ-algebra β of subsets of X which includes the Borel sets, and μ* the outer measure associated with μ (μ*(A)=Inf{(μ(B):⊃A, B ∈ μ}).

Downloads

Download data is not yet available.

Downloads

Published

1975-12-01

How to Cite

Khurana, S. S. (1975). Weak Integration of Vector-Valued Functions. The Journal of the Indian Mathematical Society, 39(1-4), 155–166. Retrieved from https://informaticsjournals.com/index.php/jims/article/view/16643

Issue

Volume 39, Issue 1-4, March-December 1975

Section

Articles

License

Copyright (c) 1975 Surjit Singh Khurana

Creative Commons License

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

 

References

R.G. BARTLE AND L.M. GRAVES, Mapping between function spaces, Trans. Amer. Math. Soc. 72 (1952), 400-^113.

LA. BEREZANSKII, Measures on uniform spaces and molecular measures, Trans. Moscow Math. Soc. 19 1968), 1-40.

N. BOURBAKI, Integration, Chapter 6, Hermann, Paris (1965).

D.B. DIMITROV, A remark on Gelfand integral, Funktsional'nyl Analizi egv Prilozheniya, 5 (1971), 84-85.

N. DINCULEANU, Vector Measures, Pergamon Press, New York (1967).

N. DUNFORD, On uniformity in linear spaces, Trans. Amer. Math. Soc. 44(1938), 305-356.

R.E. EDWARDS, Functional Analysis, Holt, Reinhart and Winston, New York (1965).

L. GILLMAN AND M. JERISON, Rings of Continuous Functions, D. van Nostrand, New York (1960).

P.R. HALMOS, Measure Theory, D. van Nostrand, New York (1950).

D. LANDERS AND L. ROGGE, The Hahn-Vitali-Saks and the uniform boundedness theorem in topological groups, Manus. Math. 4(1971), 351-359.

E. MARCZEWSKI AND R. SIKORSKI, Measures on non-separable metric spaces, Colloq. Math. 1-2 (1948), 133-139.

A. PELCZYNSKI AND C. BESSAGGA, On bases and unconditional convergence in normed iinear spaces, Studia Math. 17 (1958), 151-164.

B.J. PETTIS, On integration in vector spaces, Trans. Amer. Math. Soc. 44(1938), 277-304.

J.D. PRYCE, A device of R.J. Whitley applied to pointwise cempactness in spaces of continuous functions, Proc. London Math. Soc. 23 (1971), 532-546.

H.H. SCHAEFER, Topological Vector Spaces, Macmillan, New York (1966).

D. SONDERMAN, Masse auf Iokalbeschr'ankten Raumen, Ann. I'Inst. Fourier (Grenoble), 19(1970), 33-113.

G. ERIK THOMAS, L'Integration par rapport a une mseurede Radon vectorieile, Ann. Institut Fourier (Grenoble) 20(1970).

F. TOPS^E, Topology and measure, Lecture Notes in Math., 133 (1970), SpringerVerlag, New York.

V.S. VARADARAJAN, Measures on topological spaces, Amer. Math. Soc. Transl. Ser. 2, 48(1965), 161-220.