Christensen measurable solutions of some functional equation

Let XX be a separable FF-space over the field KK of reals or complex numbers. We characterize solutions of the equation f(x+M(f(x))y)=f(x)f(y)f(x+M(f(x))y)=f(x)f(y) in the class of functions M:K→KM:K→K and Christensen measurable functions f:X→Kf:X→K.