The Li–Yorke theorem and infinite discontinuities

Balance and discontinuities in infinite games with type-dependent strategies

Under study are games in which players receive private signals and then simultaneously choose actions from compact sets. Payoffs are measurable in signals and jointly continuous in actions. Stinchcombe (2011) [19] proves the existence of correlated equilibria for this class of games. This paper is a study of the information structures for these games, the discontinuous expected utility function...

Ordinal Analysis and the Infinite Ramsey Theorem

The infinite Ramsey theorem is known to be equivalent to the statement ‘for every set X and natural number n, the n-th Turing jump of X exists’, over RCA0 due to results of Jockusch [5]. By subjecting the theory RCA0 augmented by the latter statement to an ordinal analysis, we give a direct proof of the fact that the infinite Ramsey theorem has proof-theoretic strength εω. The upper bound is ob...

Extending the Support Theorem to Infinite Dimensions

Abstract. The Radon transform is one of the most useful and applicable tools in functional analysis. First constructed by John Radon in 1917 [9] it has now been adapted to several settings. One of the principle theorems involving the Radon transform is the Support Theorem. In this paper, we discuss how the Radon transform can be constructed in the white noise setting. We also develop a Support ...

The Infinite Dimensional Restricted Invertibility Theorem

The 1987 Bourgain-Tzafriri Restricted Invertibility Theorem is one of the most celebrated theorems in analysis. At the time of their work, the authors raised the question of a possible infinite dimensional version of the theorem. In this paper, we will give a quite general definition of restricted invertibility for operators on infinite dimensional Hilbert spaces based on the notion of density ...

An Infinite Dimensional Convolution Theorem