Hi PF I try to understand how we get get a Taylor expansion of a non linear functional. I found this good paper here F maps functions to scalars. F[f] is defined. It has not scalars as arguments. I agree with A13 and A18. In another paper (in french) skip to page 9 the fisrt term is ##\int dx P_0 (x)## and all the terms have one more variable. Do you understand the second point of view? we did not start with densities.