In this note we study generalized differentiability of functions on a class of fractals in Euclidean spaces. Such sets are not necessarily self-similar, but satisfy a weaker “scale-similar” property; in particular, they include the non self similar carpets introduced by Mackay–Tyson– Wildrick [12] but with different scale ratios. Specifically we identify certain geometric criteria for these fractals and, in the case that they have zero Lebesgue measure, we show that such fractals cannot support nonzero derivations in the sense of Weaver [16]. As a result (Theorem 26) such fractals cannot support Alberti representations and in particular, they cannot be Lipschitz differentiability spaces in the sense of Cheeger [3] and Keith [9].
