(Correspd.) Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw and Centre for Research and Development, Polish Telecom Co., Obrzezna 7, 02-691 Warsaw. e-mail: pwoj@beta.mimuw ...
We present a simple proof of Mallat's theorem about wavelet and multiresolution analysis. We do not use Fourier transform and the proof is accesible even for younger undergraduate students.