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Journal of Statistical Theory and Practice

, Volume 5, Issue 3, pp 497–513 | Cite as

A Green Proof of Fatou’s Theorem

Article

Abstract

This paper is an exposition of some applications of Stochastic Processes to boundary behavior problems for harmonic functions. As an illustration, we give a proof of Fatou’s theorem in simply connected plane domains which is probabilistic and does not use the Riemann mapping theorem. The paper closes with some remarks on further related work and open questions.

AMS Subject Classification

31A20 60J45 

Keywords

Stochastic methods in potential theory Fatou’s theorem Boundary behaviour of harmonic functions 

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Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  1. 1.Department of MathematicsClaremont McKenna CollegeClaremontUSA

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