Polar $\sigma$ideals of compact sets
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 by Gabriel Debs PDF
 Trans. Amer. Math. Soc. 347 (1995), 317338 Request permission
Abstract:
Let $E$ be a metric compact space. We consider the space $\mathcal {K}(E)$ of all compact subsets of $E$ endowed with the topology of the Hausdorff metric and the space $\mathcal {M}(E)$ of all positive measures on $E$ endowed with its natural ${w^{\ast }}$topology. We study $\sigma$ideals of $\mathcal {K}(E)$ of the form $I = {I_P} = \{ K \in \mathcal {K}(E):\mu (K) = 0,\;\forall \mu \in P\}$ where $P$ is a given family of positive measures on $E$. If $M$ is the maximal family such that $I = {I_M}$, then $M$ is a band. We prove that several descriptive properties of $I$: being Borel, and having a Borel basis, having a Borel polaritybasis, can be expressed by properties of the band $M$ or of the orthogonal band $Mâ€™$.References

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Additional Information
 © Copyright 1995 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 347 (1995), 317338
 MSC: Primary 28A12; Secondary 04A15, 28A15, 46A55
 DOI: https://doi.org/10.1090/S00029947199512672224
 MathSciNet review: 1267222