Fatou's Lemma in Several Dimensions1
نویسنده
چکیده
In this note the following generalization of Fatou's lemma is proved: Lemma. Let {fn)n_l be a sequence of integrable functions on a measure space S with values in R+, the nonnegative orthant of a d-dimensional Euclidean space, for which ffn—*aGiR+. Then there exists an integrable function f, from S to R+, such that a.e. f(s) is a limit point of VnisV^and ff^a.
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تاریخ انتشار 2010