  A generalization of the 1935 Einstein-Podolsky-Rosen (EPR) argument for
measurements with continuous variable outcomes is presented to establish
criteria for the demonstration of the EPR paradox, for situations where the
correlation between spatially separated subsystems is not perfect. Two types of
criteria for EPR correlations are determined. The first type are based on
measurements of the variances of conditional probability distributions and are
necessary to reflect directly the situation of the original EPR paradox. The
second weaker set of EPR criteria are based on the proven failure of
(Bell-type) local realistic theories which could be consistent with a local
quantum description for each subsystem. The relationship with criteria
sufficient to prove entanglement is established, to show that any demonstration
of EPR correlations will also signify entanglement. It is also shown how a
demonstration of entanglement between two spatially separated subsystems, if
not able to interpreted as a violation of a Bell-type inequality, may be
interpreted as a demonstration of the EPR correlations. In particular it is
explained how the experimental observation of two-mode squeezing using
spatially separated detectors will signify not only entanglement but EPR
correlations defined in a general sense.
