Abstract: We elucidate the connection between different notions of differentiability in P2(Rd): some have been introduced intrinsically by Ambrosio–Gigli–Savaré, the other notion due to Lions, is extrinsic and arises from the identification of P2(Rd) with the Hilbert space of square-integrable random variables. We mention potential applications such as uniqueness of viscosity solutions for Hamilton-Jacobi equations in P2(Rd), the latter not known to satisfy the Radon–Nikodym property.

(This talk is based on a work in progress with A Tudorascu).