A complete characterization of coefficients of a.e. convergent orthogonal series and majorizing measures (Q848718)

The author gives a detailed proof of a characterization of sequences of numbers \((a_{n})\) such that the series \(\sum_{n\geq 1}a_{n}\Phi_{n}\) converges a.e. for any orthonormal system \((\Phi_{n})\) in any \(L_{2}\)-space. In this characterization the author uses the set \(A=\{\sum_{m\geq n}|a_{m}|^2\,;\,n\geq 1\}\), majorizing measures on \(A\) and new descriptions of the complexity of \(A\).