\(G_{\delta }\) ideals of compact sets
type: Item
instance of: scholarly article
title: \(G_{\delta }\) ideals of compact sets
zbMATH Open document ID: 1221.03046
DOI: 10.4171/JEMS/268
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2011-07-12T00:00:00Z
review text: Summary: We investigate the structure of \(G_{\delta }\) ideals of compact sets. We define a class of \(G_{\delta }\) ideals of compact sets that, on the one hand, avoids certain phenomena present among general \(G_{\delta }\) ideals of compact sets and, on the other hand, includes all naturally occurring \(G_{\delta }\) ideals of compact sets. We prove structural theorems for ideals in this class, and we describe how this class is placed among all \(G_{\delta }\) ideals. In particular, we establish a result representing ideals in this class via the meager ideal. This result is analogous to Choquet's theorem representing alternating capacities of order \(\infty \) via Borel probability measures. Methods coming from the structure theory of Banach spaces are used in constructing examples of \(G_{\delta }\) ideals outside of our class that are important to us.
Mathematics Subject Classification ID: 03E15
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 54H05
zbMATH DE Number: 5919464
zbMATH Keywords: ideals of compact sets
author: Sławomir Solecki
MaRDI profile type: Publication
cites work: Ramsey methods in analysis
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cites work: The Structure of σ-Ideals of Compact Sets
full work available at URL: https://doi.org/10.4171/jems/268
OpenAlex ID: W2072287568
description: scientific article; zbMATH DE number 5919464