Extensions and measurability in quantum measure spaces (Q2822870)

In this paper, given a D-lattice \(E\), a \(\sigma \)-D-sublattice \(F\) of \(E\) and a function \(\mu \) on \(F\) vanishing at \(0\), the authors introduce outer and inner measures type-associated to \(\mu \) and study their properties. In the second part of the paper, given a family of couples \((E_\alpha, \mu_ \alpha)\), where each \(E_\alpha \) is a sub-D-poset of \(E\) and each \(\mu_\alpha \) is a \([0,1]\)-valued function on \(E_\alpha \) vanishing at \(0\), the authors introduce a function \(\tau \) associated to this family and use the results of the first part to obtain, in the case that \(\tau \) is \(\sigma \)-additive and a monotone extension of each \(\mu_\alpha \) to \(E\).