A study of singular points and supports of measures in reverse mathematics
type: Item
instance of: scholarly article
title: A study of singular points and supports of measures in reverse mathematics
zbMATH Open document ID: 0855.03036
DOI: 10.1016/0168-0072(95)00042-9
author: Xiaokang Yu
published in: Annals of Pure and Applied Logic
publication date: 1997-02-09T00:00:00Z
review text: The paper is a contribution to reverse mathematics. It is proved that (1) arithmetical comprehension is equivalent to the enumerability of singular points of any measure on the Cantor space, and (2) it is provable in \(\text{ACA}_0\) that any perfect closed subset of \([0, 1]\) is the support of some continuous linear functional on \(C[0, 1]\).
reviewed by: Roman Murawski
Mathematics Subject Classification ID: 03F35
zbMATH DE Number: 908473
zbMATH Keywords: reverse mathematics
zbMATH Keywords: arithmetical comprehension
zbMATH Keywords: enumerability of singular points
zbMATH Keywords: measure
zbMATH Keywords: Cantor space
zbMATH Keywords: perfect closed subset
zbMATH Keywords: support
zbMATH Keywords: continuous linear functional
MaRDI profile type: Publication
full work available at URL: 0168-0072(95)00042-9
OpenAlex ID: W1998220569
cites work: Which set existence axioms are needed to prove the separable Hahn-Banach theorem?
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cites work: Riesz representation theorem, Borel measures and subsystems of second- order arithmetic
cites work: Measure theory and weak König's lemma
description: scientific article; zbMATH DE number 908473