MontelintroducedasetoffunctionscalledanormalfamilyandusedtheseideastosimplifyclassicalresultsinfunctiontheorysuchasthemappingtheoremofRiemannandHadamard'scharacterisationofentirefunctionsoffiniteorder.Montel'sideaofnormalfamiliesprovedtobepowerfulinmanyconnections,forexampleintheproofofthePicard-Landau-Schottkytheorems,anditbecamecentralinthetheoryofiterationsofanalyticfunctionsstartedbyEmilePicardanddevelopedbyFatouandJulia.

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Montel introduced a set of functions called a normal family and used these ideas to simplify classical results in function theory such as the mapping theorem of Riemann and Hadamard 's characterisation of entire functions of finite order. Montel's idea of normal families proved to be powerful in many connections, for example in the proof of the Picard - Landau -Schottky theorems, and it became central in the theory of iterations of analytic functions started by Emile Picard and developed by Fatou and Julia .