On measurable spaces and measurable maps

Rok, strany: 2004, 125 - 140

We introduce and study the category ID the objects of which are suitable convergence D-posets of maps into the closed unit interval $I$ and the morphisms of which are sequentially continuous D-homomorphisms. We show that ID is dual to a subcategory of the category MID of generalized measurable spaces and generalized measurable maps. We construct epireflective and monocoreflective subcategories of ID and MID corresponding to two important properties of objects in ID, soberness and sequential closedness. The subcategories play important roles in applications to probability. We generalize some basic probability notions so that the generalized random variables are dual to generalized observables and generalized probability measures are ID-morphisms. Let $I_u$ be an ultrapower of $I$. We modify some of the previous results replacing $I$ by $I_u$ and replacing the sequential convergence by the approximation: a sequence approximates a point in $I_u$ whenever the sequence of standard parts converges to the standard part of the point in $I$.

ISO 690:

Papčo, M. 2004. On measurable spaces and measurable maps. In Tatra Mountains Mathematical Publications, vol. 28, no.1, pp. 125-140. 1210-3195.

APA:

Papčo, M. (2004). On measurable spaces and measurable maps. Tatra Mountains Mathematical Publications, 28(1), 125-140. 1210-3195.