In Wikipedia, there are three versions of Riesz theorems:
1 The Hilbert space representation theorem for the (continuous) dual space of a Hilbert space;
2 The representation theorem for positive linear functionals on $C_c(X)$, where $X$ is a locally compact Hausdorff space;
3 The representation theorem for the dual of $C_0(X)$, where $X$ is a locally compact Hausdorff space.
I was wondering
- if none of the three versions is more general than the others, in the sense that no one can be derived from another?
- when two or three of them can coincide?
Thanks and regards!