Espaces de fonctions ponderables

The main theorems solve two problems about weighted spacesC ₀ V(T) of continuous functions on a completely regular spaceT. These problems were first raised by W. H. Summers who solved them for the locally compact case. The first theorem gives necessary and sufficient conditions onT forC ₀ V(T) to be complete for the weighted topology; the second one shows that continuous linear functionals onC ₀ V(T) can be represented by means of measures onT.