Topics in Almost Everywhere Convergence

This chapter may require, if not more maturity, at least more stamina on the part of the reader than the preceding chapters. However, a familiarity with the contents of the fourth chapter should provide adequate foundation for a further study of Carle-son's work on the a.e. convergence of Fourier series and the subsequent work of R. Hunt. These notes do not aspire to be a complete account of almost everywhere convergence results. The basic criterion followed in the selection of the topics has been that the author felt he could at least make a contribution in the exposition of the material, when not in the content.