THE REPRESENTATION OF MEASURABLE FUNCTIONS BY SERIES

Abstract

CONTENTSIntroduction § 1. Definitions and auxiliary propositions § 2. Proof of the fundamental lemmas § 3. Representation of measurable functions in series in terms of bases of the Lp spaces § 4. Null-series § 5. Representation of measurable functions in series in terms of Haar's functions § 6. Complete systems in the sense of convergence in measure § 7. Representation of measurable functions in series in terms of complete systems in the sense of convergence in measure § 8. Convergence of orthogonal series to +∞ § 9. Universal series § 10. Unsolved problemsReferences