Measure theory based on lattices and transfinite recursion

摘要

In this methodological study we develop the foundations of mea-sure theory using lattices as prime structures instead of rings. Topological aswell as abstract regularity is incorporated into this approach from the out-set. The use of inner and outer measures is replaced by transfinite construc-tions. Basic extension steps are transfinitely iterated to yield generalizationsof Caratheodory's theorem which are optimal with respect to inner and outerapproximations