Nonlinear approximation of functions from the class $L^r$ with respect to the Vilenkin system

In this paper we prove that for any function $f$ from the class $L^r$ on $[0,1)$ one can find a function $g$ from the same class (which differs from $f$ on a set of arbitrarily small measure) whose greedy algorithm with respect to the Vilenkin system converges to $f$.