  The discussion of Fractional dimensional Hilbert spaces in the context of
Haldane exclusion statistics is extended from the case \cite{IG} of $g=1/p$ for
the statistical parameter to the case of rational $g=q/p$ with $q,p$-coprime
positive integers. The corresponding statistical mechanics for a gas of such
particles is constructed. This procedure is used to define the statistical
mechanics for particles with irrational $g$. Applications to strongly
correlated systems such as the Hubbard and $t-J$ models are discussed.
