Hilbert space theoretic methods in the study of correlation measures.

We study the uniqueness of the association of a classical statistical mechanical state and its sequence of modified correlation measures by studying a cyclic representation of the canonically associated Börchers algebra of the system. We show that semi-analyticity of the cyclic vector for a particular family of symmetric operators is sufficient for uniqueness while analyticity of the cyclic vector permits us to recover the state from the modified correlation measures. [ABSTRACT FROM AUTHOR]