Entropic projections and dominating points are solutions to convex
minimization problems related to conditional laws of large
numbers. They appear in many areas of applied mathematics such as
statistical physics, information theory, mathematical statistics,
ill-posed inverse problems or large deviation theory. By means of convex conjugate
duality and functional analysis, criteria are derived for the
existence of entropic projections, generalized entropic
projections and dominating points. Representations of the
generalized entropic projections are obtained. It is shown that
they are the “measure component" of the solutions to some
extended entropy minimization problem. This approach leads to new
results and offers a unifying point of view. It also permits to
extend previous results on the subject by removing unnecessary
topological restrictions. As a by-product, new proofs of already
known results are provided.