Borel extensions of Baire measures

J. Aldaz

Fundamenta Mathematicae (1997)

  • Volume: 154, Issue: 3, page 275-293
  • ISSN: 0016-2736

Abstract

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We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space is Mařík, that under "c is real-valued measurable", a Baire subset of a Mařík space need not be Mařík, and finally, that the preimage of a Mařík space under an open perfect map is Mařík.

How to cite

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Aldaz, J.. "Borel extensions of Baire measures." Fundamenta Mathematicae 154.3 (1997): 275-293. <http://eudml.org/doc/212238>.

@article{Aldaz1997,
abstract = {We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space is Mařík, that under "c is real-valued measurable", a Baire subset of a Mařík space need not be Mařík, and finally, that the preimage of a Mařík space under an open perfect map is Mařík.},
author = {Aldaz, J.},
journal = {Fundamenta Mathematicae},
keywords = {Mařík; quasi-Mařík; countably metacompact; Dowker; Baire measure; extension; metacompact space; Borel measure; Dowker space; Dowker-Mařík space},
language = {eng},
number = {3},
pages = {275-293},
title = {Borel extensions of Baire measures},
url = {http://eudml.org/doc/212238},
volume = {154},
year = {1997},
}

TY - JOUR
AU - Aldaz, J.
TI - Borel extensions of Baire measures
JO - Fundamenta Mathematicae
PY - 1997
VL - 154
IS - 3
SP - 275
EP - 293
AB - We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space is Mařík, that under "c is real-valued measurable", a Baire subset of a Mařík space need not be Mařík, and finally, that the preimage of a Mařík space under an open perfect map is Mařík.
LA - eng
KW - Mařík; quasi-Mařík; countably metacompact; Dowker; Baire measure; extension; metacompact space; Borel measure; Dowker space; Dowker-Mařík space
UR - http://eudml.org/doc/212238
ER -

References

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