On transformations by dyadic martingale structure preserving functions

Abstract. The concept of dyadic martingal structure preserving functions is defined. We show that composition with such functions preserves the classes of UDMD systems, that of
\(\mathcal{A}_n \)-measurable functions, the dyadic function spaces \(L^p(\mathbb I),\ H^p(\mathbb I)\), and the Lipschitz classes \({\rm Lip}\,(\alpha,\mathbb I)\).