Random sets and their curvatures

We investigate the connection between stochastic and integral geometry. Namely, we illustrate the role of curvature measures, and the corresponding integral-geometric formulas for them, in stochastic models such as random sets or particle processes. Additionally, we work with a relatively new type of objects called DC domains and we establish their measurability in the space of closed sets of d-dimensional Euclideann space, which allows for stochastic geometry models for DC domains to be defined