Probabilistisch kompakte L-unscharfe Mengen

In the case of completely distributive lattices (L,) we establish a probabilistic version of Alexander's subbase lemma and of Tychonoff's theorem for L-fuzzy sets. As an application we obtain that probabilistic topologies induced by compact ordinary topologies are also compact; i.e. ordinary compactness is consistent with probabilistic compactness. Regarding the validity of these results a counterexample shows that the complete distributivity of (L,) cannot be replaced by a weaker distributivity condition.