Polar -ideals of compact sets
Author:
Gabriel Debs
Journal:
Trans. Amer. Math. Soc. 347 (1995), 317-338
MSC:
Primary 28A12; Secondary 04A15, 28A15, 46A55
DOI:
https://doi.org/10.1090/S0002-9947-1995-1267222-4
MathSciNet review:
1267222
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a metric compact space. We consider the space
of all compact subsets of
endowed with the topology of the Hausdorff metric and the space
of all positive measures on
endowed with its natural
-topology. We study
-ideals of
of the form
where
is a given family of positive measures on
.
If is the maximal family such that
, then
is a band. We prove that several descriptive properties of
: being Borel, and having a Borel basis, having a Borel polarity-basis, can be expressed by properties of the band
or of the orthogonal band
.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1995-1267222-4
Article copyright:
© Copyright 1995
American Mathematical Society