Abstract
The main result shows that the Rademacher theorem proved by J. Lindenstrauss and D.
Preiss in 2003 (which says that, for some pairs X, Y of Banach spaces, each Lipschitz f: X -> Y is Gamma-a.e. Fréchet differentiable) generalizes to the corresponding Stepanov theorem (which says that, for such X and Y, an arbitrary f: X -> Y is Fréchet differentiable at Gamma-almost all points at which f is Lipschitz).
We also present an abstract approach which shows an easy way how (in some cases) a theorem of Stepanov type (for vector functions) can be inferred from the corresponding theorem of Radamacher type. Finally we present Stepanov type differentiability theorems with the assumption of pointwise directional Lipschitzness.