Glivenko's theorem says that, in propositional logic, classical provability of a formula entails intuitionistic double negation that formula. We generalise from to an arbitrary nucleus, calculus inductively generated abstract consequence relation, and logic any set objects whatsoever. The resulting conservation comes with precise criteria for its validity, which allow us instantly include G\"od...

We establish that Laplace transforms of the posterior Dirichlet process converge to those limiting Brownian bridge in a neighbourhood about zero, uniformly over Glivenko-Cantelli function classes. For real-valued random variables and functions bounded variation, we strengthen this result hold for all real numbers. This last is proved via an explicit strong approximation coupling inequality.

This paper provides a construction of an uncountable family of i.i.d. random vectors, indexed by the points of a nonatomic measure space, such that (a) samples are measurable functions from the index space, and (b) an exact analogue of the Glivenko-Cantelli theorem holds with respect to the measure on that space. That is, a sample possesses a.s. the same distribution as that of the random vecto...

In this paper, we investigate the convergence of empirical processes for a class of interacting particle numerical schemes arising in biology, genetic algorithms and advanced signal processing. The Glivenko-Cantelli and Donsker theorems presented in this work extend the corresponding statements in the classical theory and apply to a class of genetic type particle numerical schemes of the non-li...

In this paper we study the dense elements and the radical of a residuated lattice, residuated lattices with lifting Boolean center, simple, local, semilocal and quasi-local residuated lattices. BL-algebras have lifting Boolean center; moreover, Glivenko residuated lattices which fulfill the equation (¬ a → ¬ b) → ¬ b = (¬ b → ¬ a) → ¬ a have lifting Boolean center.

2 Glivenko-Cantelli Classes 5 2.1 The classical approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 The symmetrization procedure . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 Covering numbers and complexity estimates . . . . . . . . . . . . . . 9 2.2 Combinatorial parameters and covering numbers . . . . . . . . . . . . . . . 12 2.2.1 Uniform entropy and the VC dimen...