A game with a continuum of players is described by a function assigning payoff functions to players and satisfying some measurability properties. In this note we establish the equivalence between several measurability assumptions that have been made in the literature. Journal of Economic Literature Classification Numbers: C72.

I examine the implementation of core allocations when agents are differently informed. A one state deviation principle (an allocation cannot be improved at any state) and measurability restrictions (blocking allocations may only be measurable with respect to each agent’s private information) are sufficient to yield interim core solutions that are Bayesian implementable. Private measurability of...

It is well-known that if we assume a large class of sets of reals to be determined then we may conclude that all sets in this class have certain regularity properties: we say that determinacy implies regularity properties classwise. In [Lö05] the pointwise relation between determinacy and certain regularity properties (namely the Marczewski-Burstin algebra of arboreal forcing notions and a corr...