Orlicz–Pettis theorem
id:
orlicz-pettis-theorem-289-802848
title:
Orlicz–Pettis theorem
text:
A theorem in functional analysis concerning convergent series (Orlicz) or, equivalently, countable additivity of measures (Pettis) with values in abstract spaces. Let X be a Hausdorff locally convex topological vector space with dual X ∗ . A series ∑ n = 1 ∞ x n is subseries convergent, if all its subseries ∑ k = 1 ∞ x n k are convergent. The theorem says that, equivalently, (i) If a series ∑ n = 1 ∞ x n is weakly subseries convergent in X , then it is (subseries) convergent; or
(ii) Let A
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https://en.wikipedia.org/wiki/Orlicz%E2%80%93Pettis_theorem
date created:
date modified:
2024-01-18T19:01:38Z
main entity:
{"identifier":"Q1621180","url":"https://www.wikidata.org/entity/Q1621180"}
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