The topology of almost uniform convergence

Uniform Topology on Types and Strategic Convergence∗

We study the continuity of the correspondence of interim ε-rationalizable actions in incomplete information games. We introduce a topology on types, called uniformweak topology, under which two types of a player are close if they have similar firstorder beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity is uniform...

UNIFORM AND SEMI-UNIFORM TOPOLOGY ON GENERAL FUZZY AUTOMATA

In this paper, we dene the concepts of compatibility between twofuzzy subsets on Q, the set of states of a max- min general fuzzy automatonand transitivity in a max-min general fuzzy automaton. We then construct auniform structure on Q, and dene a topology on it. We also dene the conceptof semi-uniform structures on a nonempty set X and construct a semi-uniformstructure on the set of states of ...

On the uniform almost sure convergence of losses for the repetition of a statistical decision problem

Uniform almost everywhere domination

We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the prooftheoretic strength of the regularity of Lebesgue measure for Gδ ...

On the weak convergence of the kernel density estimator in the uniform topology

The pointwise asymptotic properties of the Parzen-Rosenblatt kernel estimator f̂n of a probability density function f on Rd have received great attention, and so have its integrated or uniform errors. It has been pointed out in a couple of recent works that the weak convergence of its centered and rescaled versions in a weighted Lebesgue Lp space, 1 ≤ p < ∞, considered to be a difficult problem,...