Full Measure Subset Research Articles

Fully generic sequences and a multiple-term return-times theorem

The return-times theorem of Bourgain, Furstenberg, Katznelson, and Ornstein states: Theorem [BFKO]. Given any measure-preserving transformation of a probability space and , there is a subset of full measure so that for any and second dynamical system and , there is a subset of full measure so that for any , We will prove here a multiple term version of this result first proposed by I. Assani. This will be accomplished by recasting the result completely as a fact about infinite names in where is a compact metrizable space. We define what it means for such an infinite name to be fully generic for some shift invariant measure. The core result here is Theorem 1 which verifies that if is fully generic in some then the collection of names for which the pair is fully generic in will have measure one with respect to any shift-invariant measure. The multiple term return-times theorem is an obvious induction on this statement. By replacing the role played by -orthogonality in the proofs in [BFKO] and [R2] by a disjointness result on joinings the argument avoids the need to identify distinguished factor algebras for the higher term averages.

Existence of a Pareto-optimal equilibrium in nearly-stationary overlapping-generations economies

In overlapping-generations models of fiat money, the existence of a Pareto-optimal equilibrium — which defines an optimal quantity of money — is more general than well-known counter-examples suggest. Those examples, having no optimal equilibrium just because there are small variations in households' tastes and endowments across generations, are not typical. On the contrary: For an open-dense, full-measure subset of smooth stationary economies and an open-dense subset of continuous stationary economies, introducing small variations in tastes and endowments across generations preserves the existence of an optimal equilibrium. Put simply, optimal equilibria generically exist for nearly-stationary economies.