# On Pettis integral and Radon measures

Fundamenta Mathematicae (1998)

- Volume: 156, Issue: 2, page 183-195
- ISSN: 0016-2736

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topPlebanek, Grzegorz. "On Pettis integral and Radon measures." Fundamenta Mathematicae 156.2 (1998): 183-195. <http://eudml.org/doc/212267>.

@article{Plebanek1998,

abstract = {Assuming the continuum hypothesis, we construct a universally weakly measurable function from [0,1] into a dual of some weakly compactly generated Banach space, which is not Pettis integrable. This (partially) solves a problem posed by Riddle, Saab and Uhl [13]. We prove two results related to Pettis integration in dual Banach spaces. We also contribute to the problem whether it is consistent that every bounded function which is weakly measurable with respect to some Radon measure is Pettis integrable.},

author = {Plebanek, Grzegorz},

journal = {Fundamenta Mathematicae},

keywords = {Pettis integrable},

language = {eng},

number = {2},

pages = {183-195},

title = {On Pettis integral and Radon measures},

url = {http://eudml.org/doc/212267},

volume = {156},

year = {1998},

}

TY - JOUR

AU - Plebanek, Grzegorz

TI - On Pettis integral and Radon measures

JO - Fundamenta Mathematicae

PY - 1998

VL - 156

IS - 2

SP - 183

EP - 195

AB - Assuming the continuum hypothesis, we construct a universally weakly measurable function from [0,1] into a dual of some weakly compactly generated Banach space, which is not Pettis integrable. This (partially) solves a problem posed by Riddle, Saab and Uhl [13]. We prove two results related to Pettis integration in dual Banach spaces. We also contribute to the problem whether it is consistent that every bounded function which is weakly measurable with respect to some Radon measure is Pettis integrable.

LA - eng

KW - Pettis integrable

UR - http://eudml.org/doc/212267

ER -

## References

top- [1] K. T. Andrews, Universal Pettis integrability, Canad. J. Math. 37 (1985), 141-159. Zbl0618.28008
- [2] G. A. Edgar, Measurability in a Banach space II, Indiana Univ. Math. J. 28 (1979), 559-579. Zbl0418.46034
- [3] R. Frankiewicz and G. Plebanek, On nonaccessible filters in measure algebras and functionals on ${L}^{\infty}\left(\lambda \right)*$, Studia Math. 108 (1994), 191-200. Zbl0849.46018
- [4] D. H. Fremlin, Measure-additive coverings and measurable selectors, Dissertationes Math. 260 (1987). Zbl0703.28003
- [5] D. H. Fremlin, Measure algebras, in: Handbook of Boolean Algebras, J. D. Monk (ed.), North-Holand, 1989, Vol. III, Chap. 22.
- [6] D. H. Fremlin, Real-valued measurable cardinals, in: Israel Math. Conf. Proc. 6, 1993, 961-1044.
- [7] K. Kunen, Some points in βN, Math. Proc. Cambridge Philos. Soc. 80 (1975), 385-398. Zbl0345.02047
- [8] K. Kunen, Set Theory, Stud. Logic 102, North-Holland, 1980.
- [9] K. Musiał, Topics in the theory of Pettis integration, Rend. Inst. Mat. Univ. Trieste 23 (1991), 177-262. Zbl0798.46042
- [10] S. Negrepontis, Banach spaces and topology, in: Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan (eds.), North-Holland, 1984, 1045-1142.
- [11] G. Plebanek, On Pettis integrals with separable range, Colloq. Math. 64 (1993), 71-78. Zbl0823.28005
- [12] L. H. Riddle and E. Saab, On functions that are universally Pettis integrable, Illinois J. Math. 29 (1985), 509-531. Zbl0576.46034
- [13] L. H. Riddle, E. Saab and J. J. Uhl, Sets with the weak Radon-Nikodym property in dual Banach spaces, Indiana Univ. Math. J. 32 (1983), 527-541. Zbl0547.46009
- [14] G. F. Stefansson, Universal Pettis integrability, Proc. Amer. Math. Soc. 125 (1993), 1431-1435.
- [15] M. Talagrand, Pettis integral and measure theory, Mem. Amer. Math. Soc. 51 (1984).
- [16] G. Vera, Pointwise compactness and continuity of the integral, Rev. Mat. (1996) (numero supl.), 221-245. Zbl0873.28005

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