  We formulate a simple characterization of homogeneous Young measures
associated with measurable functions. It is based on the notion of the
quasi-Young measure introduced in the previous article published in this
Journal. First, homogeneous Young measures associated with the measurable
functions are recognized as the constant mappings defined on the domain of the
underlying function with values in the space of probability measures on the
range of these functions. Then the characterization of homogeneous Young
measures via image measures is formulated. Finally, we investigate the
connections between weak convergence of the homogeneous Young measures
understood as elements of the Banach space of scalar valued measures and the
weak* L1 sequential convergence of their densities. A scalar case of the smooth
functions and their Young measures being Lebesgue-Stieltjes measures is also
analyzed.
