  It has also been suggested, in view of Boltzmann's later habit of discretising continuous variables, that he somehow thought of the energy hypersurface as a discrete manifold containing only finitely many discrete cells (Gallavotti 1994).  In this reading, obviously, the mathematical no-go theorems of Rozenthal and Plancherel no longer apply. Now it is definitely true that Boltzmann developed a preference towards discretizing continuous variables, and would later apply this procedure more and more (although usually adding that this was purely for purposes of illustration and more easy understanding). However, there is no evidence in the (1868) and (1871b) papers that Boltzmann implicitly assumed a discrete structure of mechanical phase space or the energy hypersurface.