4 окт. 2017 г. · Theorem (Vitali): Suppose that the family {f1,...,fn} of analytic maps is normal in a domain D and that fn converges pointwise to some ...

16 апр. 2018 г. · By Vitali's theorem there is a subsequence of this subsequence which converges uniformly on compact sets to some analytic function g. ... complex- ...

7 авг. 2013 г. · Then fn(z) tends uniformly to a limit in any region bounded by a contour interior to D, the limit being, therefore, an analytic function of z.

24 февр. 2012 г. · This is an exercise from Rudin's Real and Complex Analysis. Prove the following convergence theorem of Vitali: Let μ(X)<∞ and suppose a ...

10 апр. 2018 г. · The Vitali Convergence Theorem remain valid if pointwise convergence ae is replaced by convergence in measure.

17 сент. 2020 г. · The first formulation is a strong result that is related with Picard's little theorem (in the sense that Picard's little theorem is a corollary of its methods ...

13 апр. 2012 г. · By construction of the An, it is easily seen that S converges pointwise to 0. So, S satisfies the hypotheses of the Vitali Convergence Theorem.

2 дек. 2015 г. · You can apply Vitali (at least if the measure space is finite), but the dominated convergence theorem is not applicable in general.

13 мая 2019 г. · Given the assumptions of the Vitali-Porter Theorem, but assume A does not have an accumulation point in G. Show that there exists a locally ...

30 апр. 2020 г. · My question is the following: could we deduce something like Vitali or Osgood theorem using only pointwise convergence on a dense set D? Thank ...