ON FINITE DIMENSIONAL FATOU'S LEMMA.

The following generalization of Fatous 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 fs is a limit point of f sub ns. When d 1, one has an equivalent form of Fatous lemma. Author