On Pettis integral and Radon measures

Grzegorz Plebanek

Fundamenta Mathematicae (1998)

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

Abstract

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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.

How to cite

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Plebanek, 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

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  10. [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. [11] G. Plebanek, On Pettis integrals with separable range, Colloq. Math. 64 (1993), 71-78. Zbl0823.28005
  12. [12] L. H. Riddle and E. Saab, On functions that are universally Pettis integrable, Illinois J. Math. 29 (1985), 509-531. Zbl0576.46034
  13. [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. [14] G. F. Stefansson, Universal Pettis integrability, Proc. Amer. Math. Soc. 125 (1993), 1431-1435. 
  15. [15] M. Talagrand, Pettis integral and measure theory, Mem. Amer. Math. Soc. 51 (1984). 
  16. [16] G. Vera, Pointwise compactness and continuity of the integral, Rev. Mat. (1996) (numero supl.), 221-245. Zbl0873.28005

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