Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Fatou's lemma in several dimensions

Author: David Schmeidler
Journal: Proc. Amer. Math. Soc. 24 (1970), 300-306
MSC: Primary 28.25
MathSciNet review: 0248316
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note the following generalization of Fatou's lemma is proved:

Lemma. Let $ ({f_n})_{n - 1}^\infty $ be a sequence of integrable functions on a measure space $ S$ with values in $ R_ + ^d$, the nonnegative orthant of a $ d$-dimensional Euclidean space, for which $ \int {{f_n} \to a \in R_ + ^d} $. Then there exists an integrable function $ f$, from $ S$ to $ R_ + ^d$, such that a.e. $ f(s)$ is a limit point of $ ({f_n}(s))_{n - 1}^\infty $ and $ \int {f \leqq a} $.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28.25

Retrieve articles in all journals with MSC: 28.25

Additional Information

PII: S 0002-9939(1970)0248316-7
Keywords: Fatou lemma, vector valued integrals
Article copyright: © Copyright 1970 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia