Provision of a discrete public good with infinitely-many commodities

Suppose a group of individuals must decide whether to undertake a public project. The private commodity space, from which are also drawn the inputs for the public good, exhibits the Riesz decomposition property. We give a sufficient condition for the existence of a feasible provision of the public good that Pareto-dominates inaction. The condition is that the `net benefit' from the public project be positive. If this condition is met, by the Riesz decomposition property the cost of the project can be decomposed into a sum of individual contributions or taxes so that the project can be `financed' and every agent retains a positive surplus.