  The properties of statistical ensembles with abelian charges close to the
thermodynamic limit are discussed. The finite volume corrections to the
probability distributions and particle density moments are calculated. Results
are obtained for statistical ensembles with both exact and average charge
conservation. A new class of variables (semi--intensive variables) which differ
in the thermodynamic limit depending on how charge conservation is implemented
in the system is introduced. The thermodynamic limit behavior of these
variables is calculated through the next to leading order finite volume
corrections to the corresponding probability density distributions.
