  To describe a set of functions, which forms a reflexive subspace B of the
classical Banach space L a special function that characterizes their average
integral growth is introduced. It is shown that this function essentially
depends on the geometry of B. By the way, one question of la Vallee Poussin is
answered. Also a short proof of the known result about the existence of an
uncomplemented subspace isomorphic to the Hilbert space in every Lebesgue -
Riesz space Lp (1<p<2) is obtained.
