ON FINITE DIMENSIONAL FATOU'S LEMMA.
Abstract
The following generalization of Fatou's lemma is proven: Lemma: Let (f sub n) be a sequence of integrable functions on a measure space S with values in the non negative orthant of a d-dimensional Euclidean space, for which the integral of (f sub n) (arrow) (1,...,1), n = 1,2,... Then there exists an integrable function f such that the integral of f = or < (1,...,1) and for a.e. s in S f(s) is a limit point of (f sub n(s)). When d = 1, one has an equivalent form of Fatou's lemma. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1968
- Accession Number
- AD0680789
Entities
People
- David Schmeidler
Organizations
- Hebrew University of Jerusalem