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The theory on the Uniqueness of Meromorphic Functions is that under what condition, two meromorphic functions can be identical. What will be studied in this article is the theory on the uniqueness of two meromorphic functions sharing 3 sets. We come to this conclusion readily: there is a set S with 5 elements. If f ( z ) and g ( z ) are two nonconstant meromorphic functions satisfying E ( S , f ) = E ( S ,g),E ( {0 } , f ) = E ( {0 } ,g), E ( {∞} , f ) = E ( {∞} ,g), then f ( z )≡g ( z).This paper contains 4 sections. We’ll introduce some notations and fundamental results on the Nevanlinna theory in section one, and the conclusion and the background in section two. As for section three, it will state some lemmas to be used in proof of the conclusion, among which Lemma 1 to Lemma 6 are parts of the course of the proof. It is because of pithiness that they are taken out of Theorem 2.1. Section four is the detailed proof of the result of this article.
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