Universal Pettis integrability property

Stefánsson, Gunnar F.

doi:10.1090/S0002-9939-1995-1277135-5

Universal Pettis integrability property
HTML articles powered by AMS MathViewer

by Gunnar F. Stefánsson

Proc. Amer. Math. Soc. 123 (1995), 1431-1435

DOI: https://doi.org/10.1090/S0002-9939-1995-1277135-5

PDF | Request permission

Abstract:

Functions into duals and pre-duals of weakly compactly generated spaces (WCG) are studied. We show that a universally weakly measurable function f into a dual of a WCG has the RS property. Also, for such a function, we sharpen the decomposition obtained by E. M. Bator (1988). We show that bounded weakly measurable functions into pre-duals of WCG spaces are always Pettis integrable, universally weakly measurable, or not.

References

D. Amir and J. Lindenstrauss, The structure of weakly compact sets in Banach spaces, Ann. of Math. (2) 88 (1968), 35–46. MR 228983, DOI 10.2307/1970554
Elizabeth M. Bator, Pettis decomposition for universally scalarly measurable functions, Proc. Amer. Math. Soc. 104 (1988), no. 3, 795–800. MR 964859, DOI 10.1090/S0002-9939-1988-0964859-6
W. J. Davis, T. Figiel, W. B. Johnson, and A. Pełczyński, Factoring weakly compact operators, J. Functional Analysis 17 (1974), 311–327. MR 0355536, DOI 10.1016/0022-1236(74)90044-5
R. S. Phillips, Integration in a convex linear topological space, Trans. Amer. Math. Soc. 47 (1940), 114–145. MR 2707, DOI 10.1090/S0002-9947-1940-0002707-3
Lawrence H. Riddle, Elias Saab, and J. J. Uhl Jr., Sets with the weak Radon-Nikodým property in dual Banach spaces, Indiana Univ. Math. J. 32 (1983), no. 4, 527–541. MR 703283, DOI 10.1512/iumj.1983.32.32038
Gunnar F. Stefánsson, Pettis integrability, Trans. Amer. Math. Soc. 330 (1992), no. 1, 401–418. MR 1070352, DOI 10.1090/S0002-9947-1992-1070352-0
Michel Talagrand, Pettis integral and measure theory, Mem. Amer. Math. Soc. 51 (1984), no. 307, ix+224. MR 756174, DOI 10.1090/memo/0307