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In this paper we consider a problem initially posed by Yi . We prove two uniqueness theorems on meromorphic functions which improve and extend results of Lahiri  and Fang and Lahiri . We provide an example that shows that a condition in one of our results is sharp.
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Abhijit Banerjee, Uniqueness of meromorphic functions sharing two sets with finite weight. Port. Math. 65 (2008), no. 1, pp. 81–93DOI 10.4171/PM/1800