منابع مشابه
Empirical Processes: Glivenko–Cantelli Theorems
The reader is referred to Chapter 1.6 of Wellner’s Torgnon notes, Chapter ??? of VDVW and Chapter 8.3 of Kosorok. First, a theorem using bracketing entropy. Let (F , ‖ ‖) be a subset of a normed space of real functions f : X → R. Given real functions l and u on X (but not necessarily in F), the bracket [l, u] is defined as the set of all functions f ∈ F satisfying l ≤ f ≤ u. The functions l, u ...
متن کاملPreservation Theorems for Glivenko-Cantelli and Uniform Glivenko-Cantelli Classes
We show that the P−Glivenko property of classes of functions F1, . . . ,Fk is preserved by a continuous function φ from R to R in the sense that the new class of functions x → φ(f1(x), . . . , fk(x)), fi ∈ Fi, i = 1, . . . , k is again a Glivenko-Cantelli class of functions if it has an integrable envelope. We also prove an analogous result for preservation of the uniform Glivenko-Cantelli prop...
متن کاملGlivenko Type Theorems for Intuitionistic Modal Logics
In this article we deal with Glivenko type theorems for intuitionistic modal logics over Prior’s MIPC. We examine the problems which appear in proving Glivenko type theorems when passing from the intuitionistic propositional logic Int to MIPC. As a result we obtain two different versions of Glivenko’s theorem for logics over MIPC. Since MIPC can be thought of as a one-variable fragment of the i...
متن کاملGlivenko theorems for substructural logics over FL
It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko’s theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko’s theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via ...
متن کاملPreservation Theorems for Glivenko-cantelli and Uniform Glivenko-cantelli Classes Aad Van Der Vaart and Jon
We show that the P Glivenko property of classes of functions F1; : : : ;Fk is preserved by a continuous function ' from R k to R in the sense that the new class of functions x! '(f1(x); : : : ; fk(x)); fi 2 Fi; i = 1; : : : ; k is again a Glivenko-Cantelli class of functions if it has an integrable envelope. We also prove an analogous result for preservation of the uniform Glivenko-Cantelli pro...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2009
ISSN: 0168-0072
DOI: 10.1016/j.apal.2009.05.006