(2.1.17) Kvaal : It is interesting to note, that in Lieb's convex formulation of exact DFT, the essence of which is succinctly described in contribution (2.1.13), does not rely in any way on the classical Hohenberg-Kohn theorems to establish duality of ρ and v. Neither are the theorems necessary for the derivation of exact Kohn-Sham theory. While the original Hohenberg-Kohn theorems are now established rigorously, albeit with mild assumptions on the potential, it is my opinion much easier to say that the Legendre transform of E [v] is the essence and foundation of DFT, from both a mathematical and a physical point of view. Lammert has pointed out that the Hohenberg-Kohn density-potential correspondence map is quite ill-behaved. Nearby v-representable densities may have wildly different potentials, and thus fundamental arguments that rely on, for example, some kind of differentiation of v as a function of ρ are not useful, at least for exact DFT. (2.1.18) Laestadius : With recent development of uniquecontinuation from sets of measure zero, in particular by Garrigue, I regard the Hohenberg-Kohn theorem as rigorous, albeit with some limitations. In particular, certain L p spaces need to be consider for the potentials -for example, Theorem 30 in ref. 33 is a Hohenberg-Kohn result with all previous gaps filled, although it is not given for L 3/2 + L ∞ .