scholarly journals Weak sequential convergence in L1(μ, X) and an approximate version of Fatou's Lemma

1986 ◽  
Vol 114 (2) ◽  
pp. 569-573 ◽  
Author(s):  
M.Ali Khan ◽  
Mukul Majumdar
Keyword(s):  
Sequential Convergence ◽  
Fatou’S Lemma ◽  
Fatou's Lemma ◽  
Approximate Version

On Fatou's Lemma in several dimensions

1971 ◽  
Vol 17 (2) ◽  
pp. 151-155 ◽  
Author(s):  
Werner Hildenbrand ◽  
Jean -Fran�ois Mertens
Keyword(s):  
Fatou’S Lemma ◽  
Fatou's Lemma

scholarly journals Extended Real-Valued Double Sequence and Its Convergence

2015 ◽  
Vol 23 (3) ◽  
pp. 253-277 ◽  
Author(s):  
Noboru Endou
Keyword(s):  
Convergence Theorem ◽  
Double Sequence ◽  
Monotone Convergence ◽  
Double Sequences ◽  
Monotone Convergence Theorem ◽  
Fatou’S Lemma ◽  
Fatou's Lemma

Abstract In this article we introduce the convergence of extended realvalued double sequences [16], [17]. It is similar to our previous articles [15], [10]. In addition, we also prove Fatou’s lemma and the monotone convergence theorem for double sequences.

scholarly journals Fatou's Lemma and Lebesgue's convergence theorem for measures

2000 ◽  
Vol 13 (2) ◽  
pp. 137-146 ◽  
Author(s):  
Onésimo Hernández-Lerma ◽  
Jean B. Lasserre
Keyword(s):  
Asymptotic Behavior ◽  
Banach Spaces ◽  
General Result ◽  
Convergence Theorem ◽  
Convergence Theorems ◽  
Vector Lattices ◽  
Fatou’S Lemma ◽  
Dominated Convergence ◽  
Special Case ◽  
Fatou's Lemma

Analogues of Fatou's Lemma and Lebesgue's convergence theorems are established for ∫fdμn when {μn} is a sequence of measures. A “generalized” Dominated Convergence Theorem is also proved for the asymptotic behavior of ∫fndμn and the latter is shown to be a special case of a more general result established in vector lattices and related to the Dunford-Pettis property in Banach spaces.

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