The study of the structure of the set of positive deviations of meromorphic functions. I

This article is devoted to the construction of examples of functions that are meromorphic for $|z|<R$ ($R\leqslant\infty$) and whose set of positive deviations has the power of the continuum. These examples also allow us to expose the essential difference between the set of defect values of R. Nevanlinna and G. Valiron and the set of positive deviations of meromorphic functions.