The principle of large deviations for the almost everywhere central limit theorem

The purpose of the present paper is to prove a principle of large deviations for Brosamler’s functional almost everywhere central limit theorem for i.i.d. random variables on R. This principle of large deviations for the functional almost everywhere central limit theorem naturally implies a principle of large deviations for Brosamler and Schatte’s almost everywhere central limit theorem. Furthermore it implies principles of large deviations for various other almost everywhere limit theorems.