Uniqueness of measure extensions in Banach spaces

Studia Mathematica

Volumn 175, Issue 2, 2006, Pages 139-155

  Rodriguez J ^a,b   Vera, G ^a,b  

^a Universidad de Murcia ^*

^b UNIVERSITY OF MURCIA   (Spain)

Author keywords

Baire measure; Banach space; Measure extension; Pettis integral

Indexed keywords

EID: 33751433301     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm175-2-3     Document Type: Article

References (30)

1. E. M. Bator, Pettis integrability and the equality of the norms of the weak* integral and the Dunford integral, Proc. Amer. Math. Soc. 95 (1985), 265-270.
2. J. Bourgain, D. H. Fremlin, and M. Talagrand, Pointwise compact sets of Baire-measurable functions, Amer. J. Math. 100 (1978), 845-886.
3. H. H. Corson, The weak topology of a Banach space, Trans. Amer. Math. Soc. 101 (1961), 1-15.
4. R. G. Douglas, On extremal measures and subspace density, Michigan Math. J. 11 (1964), 243-246.
5. 1, CWI Tract 59, Centrum voor Wiskunde en Informatica, Amsterdam, 1989.
6. G. A. Edgar, Errata to "Measurability in a Banach space. II", available at URL http://www.math.ohio-state.edu/~edgar/publications/m2errata.ps.
7. _, Measurability in a Banach space, Indiana Univ. Math. J. 26 (1977), 663-677.
8. _, Measurability in a Banach space. II, ibid. Indiana Univ. Math. J. 28 (1979), 559-579.
9. _, On pointwise-compact sets of measurable functions, in: Measure Theory (Ober-wolfach, 1981), Lecture Notes in Math. 945, Springer, Berlin, 1982, 24-28.
10. G. A. Edgar and L. Sucheston, Stopping Times and Directed Processes, Encyclopedia Math. Appl. 47, Cambridge Univ. Press, Cambridge, 1992.
11. M. Fabian, Gâteaux Differentiability of Convex Functions and Topology. Weak Asplund Spaces, CMS Ser. Monogr. Adv. Texts, Wiley, New York, 1997.
12. D. H. Fremlin, Borel sets in nonseparable Banach spaces, Hokkaido Math. J. 9 (1980), 179-183.
13. _, Measure Theory. Vol. 4: Topological Measure Spaces, Torres Fremlin, Colchester, 2003.
14. D. H. Fremlin and M. Talagrand, A decomposition theorem for additive set-functions, with applications to Pettis integrals and ergodic means, Math. Z. 168 (1979), 117-142.
15. A. B. Gulisashvili, Estimates for the Pettis integral in interpolation spaces, and a generalization of some imbedding theorems, Soviet Math. Dokl. 25 (1982), 428-432;
16. transl. of: Dokl. Akad. Nauk SSSR 263 (1982), 793-798 (in Russian).
17. 1, Math. Proc. Cambridge Philos. Soc. 80 (1976), 269-276.
18. A. Ionescu Tulcea, On pointwise convergence, compactness, and equicontinuity. II, Adv. Math. 12 (1974), 171-177.
19. K. Musiał and G. Plebanek, Pettis integrability and the equality of the norms of the weak* integral and the Dunford integral, Hiroshima Math. J. 19 (1989), 329-332.
20. S. Negrepontis, Banach spaces and topology, in: Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, 1045-1142.
21. 1, Israel J. Math. 20 (1975), 375-384.
22. D. Plachky, Extremal and monogenic additive set functions, Proc. Amer. Math. Soc. 54 (1976), 193-196.
23. G. Plebanek, On Pettis integrals with separable range, Colloq. Math. 64 (1993), 71-78.
24. R. Pol, On a question of H. H. Corson and some related problems, Fund. Math. 109 (1980), 143-154.
25. G. F. Stefánsson, The μ-PIP and integrability of a single function, Proc. Amer. Math. Soc. 124 (1996), 539-542.
26. M. Talagrand, Compacts de fonctions mesurables et filtres non mesurables, Studia Math. 67 (1980), 13-43.
27. _, Pettis integral and measure theory, Mem. Amer. Math. Soc. 51 (1984), no. 307.
28. V. S. Varadarajan, Measures on topological spaces, Amer. Math. Soc. Transl. (2) 48 (1965), 161-228;
29. transl. of: Mat. Sb. (N.S.) 55 (97) (1961), 35-100.
30. G. Vera, Pointwise compactness and continuity of the integral, Rev. Mat. Univ. Complut. Madrid 9 (1996), Special Issue, suppl., 221-245.