An integrability theorem for unbounded Vilenkin systems (Q1307360)

We state the symmetry condition at the end of the first section, after specifying a construction of Vilenkin systems. In Section 2, we provide more information about these systems, and outline the proof of our main result. In Section 3, we complete the proof, except for two lemmas, which we prove in Section 4. We propose and analyse an alternate indexing of some Vilenkin systems in Section 5.