VITALI'S THEOREM WITHOUT UNIFORM BOUNDEDNESS

被引：2

作者：

Nguyen Quang Dieu ^{[1
]}

Phung Van Manh ^{[1
]}

Pham Hien Bang ^{[2
]}

Le Thanh Hung ^{[3
]}

机构：

[1] Hanoi Natl Univ Educ, 136 Xuan Thuy St, Hanoi, Vietnam

[2] Thai Nguyen Univ Educ, Luong Ngoc Quyen, Thai Nguyen, Vietnam

[3] Coll Educ, Trung Trac, Vinh Phuc, Vietnam

来源：

PUBLICACIONS MATEMATIQUES | 2016年 / 60卷 / 02期

关键词：

Rapid convergence; convergence in capacity; pluripolar set; relative capacity;

D O I：

10.5565/PUBLMAT_60216_03

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let {f(m)}m >= 1 be a sequence of holomorphic functions defined on a bounded domain D subset of C-n or a sequence of rational functions (1 <= deg r(m) <= m) defined on C-n. We are interested in finding sufficient conditions to ensure the convergence of {f(m)}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.

引用

页码：311 / 334

页数：24

共 11 条

[1] [Anonymous], 1994, PROGR MATH
[2] Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates
Benelkourchi, S
Jennane, B
Zeriahi, A
[J]. ARKIV FOR MATEMATIK, 2005, 43 (01): : 85 - 112
[3] Blocki Z., 2002, UNFINISHED LECT NOTE
[4] On the convergence in capacity of rational approximants
Bloom, T
[J]. CONSTRUCTIVE APPROXIMATION, 2001, 17 (01) : 91 - 102
[5] Chirka E. M., 1976, MAT SBORNIK, V99, P615
[6] COLWELL P, 1966, P AM MATH SOC, V17, P582
[7] DAVIDSON KR, 1983, AM MATH MON, V90, P391, DOI 10.2307/2975578
[8] Gonchar A. A., 1974, Mat. Sb. (N.S.), V93, P296
[9] KLIMEK M, 1991, LONDON MATH SOC MONO, V6
[10] SADULLAEV A, 1984, MATH USSR SB+, V125, P271

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