Ideals of null sets of set functions (Q2644790)

The following types of problems are studied: Given a set function v on an algebra \({\mathcal A}\subset 2^{\Omega}\), when does there exist a content (or a measure) \(\mu| {\mathcal A}\) with \(\mu\geq v\) (and \(\mu (\Omega)=v(\Omega))\) which vanishes on a given ideal of ``null sets'' of v? Some applications to core problems in cooperative game theory and to measure extension problems are sketched.