Vitali's theorem without uniform boundedness

• Autores: Nguyen Quang Dieu, Phung Van Manh, Pham Hien Bang, Le Thanh Hung
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 60, Nº 2, 2016, págs. 311-334
• Idioma: inglés
• DOI: 10.5565/10.5565-PUBLMAT_60216_03
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• Resumen

  • 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.