Vitali's theorem without uniform boundedness
Quang Dieu, Nguyen (Hanoi National University of Education)
Van Manh, Phung (Hanoi National University of Education)
Hien Bang, Pham (Thai Nguyen University of Education)
Hung, Le Thanh (College of Education (Vinh Phuc, Vietnam))

Date:	2016
Abstract:	Let {fm}m≥1 be a sequence of holomorphic functions defined on a bounded domain D ⊂ Cn or a sequence of rational functions (1 ≤ deg rm ≤ m) defined on Cn. We are interested infinding sufficient conditions to ensure the convergence of {fm}m≥1 on a large set provided the convergence holds pointwise on a not too small set. This type of result is inspired from a theorem of Vitali which gives a positive answer for uniformly bounded sequence.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Rapid convergence ; Convergence in capacity ; Pluripolar set ; Relative capacity
Published in:	Publicacions matemàtiques, Vol. 60 Núm. 2 (2016) , p. 311-334 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/311010
DOI: 10.5565/PUBLMAT_60216_03

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