On the m-term approximation in L 1(0, 1) in the Haar system.

The article considers the m-term L¹-greedy algorithm in the Haar system normalized in L¹ (0,1). It uses the binary numbering of the functions of the Haar system. It describes some notation and proves several lemmas, which will be used in the proof of the theorem. It proves the existence of a function f ε L¹ (0,1) for which there is no L¹-greedy algorithm in the Haar system converging to f.