Open Access
2016 Vitali's theorem without uniform boundedness
Nguyen Quang Dieu, Phung Van Manh, Pham Hien Bang, Le Thanh Hung
Publ. Mat. 60(2): 311-334 (2016). DOI: 10.5565/PUBLMAT_60216_03


Let $\{f_m\}_{m \ge 1}$ be a sequence of holomorphic functions defined on a bounded domain $D \subset \mathbb C^n$ or a sequence of rational functions $(1 \le \deg r_m \le m)$ defined on $\mathbb C^n$. We are interested in finding sufficient conditions to ensure the convergence of $\{f_m\}_{m \ge 1}$ 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.


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Nguyen Quang Dieu. Phung Van Manh. Pham Hien Bang. Le Thanh Hung. "Vitali's theorem without uniform boundedness." Publ. Mat. 60 (2) 311 - 334, 2016.


Received: 25 August 2014; Revised: 29 January 2015; Published: 2016
First available in Project Euclid: 11 July 2016

zbMATH: 1347.41002
MathSciNet: MR3521494
Digital Object Identifier: 10.5565/PUBLMAT_60216_03

Primary: 41A05 , 41A63 , 46A32

Keywords: convergence in capacity , pluripolar set , Rapid convergence , relative capacity

Rights: Copyright © 2016 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.60 • No. 2 • 2016
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