Two Constructions on Limits of Entropy Functions

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The correspondence between the subvectors of a random vector and their Shannon entropies gives rise to an entropy function. Limits of the entropy functions are closed to convolutions with modular polymatroids, and when integer-valued also to free expansions. The problem of description of the limits of entropy functions is reduced to those limits that correspond to matroids. Related results on entropy functions are reviewed with regard to polymatroid and matroid theories, and perfect and ideal secret sharing. </para>