Embedding measure spaces

Abstract

For a given measure space $(X,\mathcal{B},\mu )$ we construct all measure spaces $(Y,\mathcal{C},\lambda )$ in which $(X,\mathcal{B},\mu )$ is embeddable. The construction is modeled on the ultrafilter construction of the Stone--Čech compactification of a completely regular topological space. Under certain conditions the construction simplifies. Examples are given when this simplification occurs.

arXiv comment24 pages