Quasiuniversal in Orthogonal Series

Let be an orthonormal complete in L²[0, 1] system, such that const, n ≥ 1 for some p₀ > 2. In the paper a series is constructed, which is quasiuniversal with respect to rearrangements in L^p[0, 1] for any p ≥ 1. This means that for any є. such that for any p ≥ 1 and for each function f(x) ∈ L^p (E) the series can be rearranged, so that the new series converges to f (x) in L^p (E) metric.