We show that if a locally compact group G acts properly on a locally compact σ-compact space X, then there is a family of G-invariant proper continuous finite-valued pseudometrics which induces the topology of X. If X is, furthermore, metrizable, then G acts properly on X if and only if there exists a G-invariant proper compatible metric on X.

In this article a novel characterization of Bose-Einstein condensates is proposed. Instead relying on occupation numbers few dominant modes, which become macroscopic in the limit infinite particle numbers, it focuses regular excitations whose stay bounded limit. manner, subspaces global, respectively local wave functions are identified. Their orthogonal complements determine particles forming p...

Optimality conditions and comparative static properties of the optimal Mirrleesian nonlinear income tax are obtained for a nite population and quasilinear-in-consumption preferences. Contrary to Weymark (1987) who considers quasilinear-in-leisure preferences, the linearity with respect to gross income, which is observed by the government and used as a tax base, is lost. A reduced-form optimal i...