Results 221 to 230 of about 3,080 (245)
Some of the next articles are maybe not open access.
An absoluteness principle for Borel sets
The Journal of Symbolic Logic, 1998The purpose of these notes is to describe an absoluteness principle due to Jacques Stern and discuss some applications to the general study of Borel sets. This paper will not be engaged in independence results, but in proving outright theorems about the Borel hierarchy.Roughly speaking, Stern's absoluteness principle states that if a certain set can ...
openaire +2 more sources
Borel sets and circuit complexity
Proceedings of the fifteenth annual ACM symposium on Theory of computing - STOC '83, 1983It is shown that for every k, polynomial-size, depth-k Boolean circuits are more powerful than polynomial-size, depth-(k−1) Boolean circuits. Connections with a problem about Borel sets and other questions are discussed.
openaire +1 more source
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1965
Abstract The descriptive theory of Borel sets is developed for a fairly general class of spaces. For a satisfactory theory it seems to be necessary to work with a Hausdorff space subject to the condition that each open set can be expressed as a countable union of closed sets. Under this condition it is shown that the descriptive Borel
openaire +2 more sources
Abstract The descriptive theory of Borel sets is developed for a fairly general class of spaces. For a satisfactory theory it seems to be necessary to work with a Hausdorff space subject to the condition that each open set can be expressed as a countable union of closed sets. Under this condition it is shown that the descriptive Borel
openaire +2 more sources
Borel Sets, Random Variables, and Borel Functions
1990In Chapter 3, we note that the class of events is assumed to be a sigma algebra of subsets of the basic space Ω. In Appendix 2a, we characterize a sigma algebra of events as a class closed under complements and countable unions, and show that these conditions imply closure under countable intersections.
openaire +1 more source
A Linear Borel set whose Difference set is not a Borel set
Bulletin of the London Mathematical Society, 1970openaire +2 more sources
1995
Let (X,T) be a topological space. The class of Borel sets of X is the σ-algebra generated by the open sets of X. We denote it by B(X,T) (or by B(X) or B(T), when appropriate). We call (X, B(X)) the Borel space of X. If Ɛ is a countable subbasis for X, then clearly B(X) = σ(Ɛ), so B(X) is countably generated when X is second countable. Note also that if
openaire +1 more source
Let (X,T) be a topological space. The class of Borel sets of X is the σ-algebra generated by the open sets of X. We denote it by B(X,T) (or by B(X) or B(T), when appropriate). We call (X, B(X)) the Borel space of X. If Ɛ is a countable subbasis for X, then clearly B(X) = σ(Ɛ), so B(X) is countably generated when X is second countable. Note also that if
openaire +1 more source
Two Convex Borel Sets whose Convex Hull is not a Borel Set
Bulletin of the London Mathematical Society, 1974openaire +2 more sources
Isomorphism and Embedding of Borel Systems on Full Sets
Acta Applicandae Mathematicae, 2013Michael Hochman, Hochman Michael
exaly