A measure-theoretic boundary limit theorem
The authors describe in purely measure-theoretic terms, without reference to probability or harmonic functions, the convergence a.e. of an appropriate ratio of positive linear functionals of measures to their Radon-Nikodym derivative. From this result the fine limit theorem of Fatou-Naim-Doob and its extension to general potential theories follow in a few lines.
scientific article; zbMATH DE number 3973295
scientific article