Results 1 to 10 of about 6,838,637 (208)

PARTITIONING THE REAL LINE INTO BOREL SETS [PDF]

The Journal of Symbolic Logic, 2021
For which infinite cardinals $\kappa $ is there a partition of the real line ${\mathbb R}$ into precisely $\kappa $ Borel sets? Work of Lusin, Souslin, and Hausdorff shows that ${\mathbb R}$ can be partitioned into $\aleph _1$ Borel sets.
W. Brian
semanticscholar   +4 more sources

On omega context free languages which are Borel sets of infinite rank [PDF]

Theoretical Computer Science, 2003
This paper is a continuation of the study of topological properties of omega context free languages (?-CFL). We proved in (Topological properties of omega context free languages, Theoretical Computer Science, 262 (1?2) (2001) 669?697) that the class of ?-
Olivier Finkel
exaly   +2 more sources

Borel sets and circuit complexity

Proceedings of the fifteenth annual ACM symposium on Theory of computing - STOC '83, 1983
It 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.
M. Sipser
semanticscholar   +2 more sources

Borel Sets Via Games

Annals of Probability, 1981
A family of games $G = G(\sigma, u)$ is defined such that (a) for each $\sigma$ the set of all $u$ for which Player I can force a win in $G(\sigma, u)$ is a Borel set $B(u)$ and (b) every Borel set is a $B(u)$ for some $u$.
exaly   +4 more sources

Exponential Iteration and Borel Sets

Computational Methods and Function Theory
We determine the exact Borel class of the points whose iterates under $\exp(z)+a$ tend to infinity. We also prove that the sets of non-escaping Julia points for many of these functions are topologically equivalent.
David Lipham
exaly   +3 more sources

Borel sets of Rado graphs and Ramsey's theorem [PDF]

European journal of combinatorics (Print), 2019
The well-known Galvin-Prikry Theorem states that Borel subsets of the Baire space are Ramsey: Given any Borel subset $\mathcal{X}\subseteq [\omega]^{\omega}$, where $[\omega]^{\omega}$ is endowed with the metric topology, each infinite subset $X\subseteq
Natasha Dobrinen
semanticscholar   +1 more source

Frucht’s theorem in Borel setting

Periodica Mathematica Hungarica, 2023
In this paper, we show that Frucht's theorem holds in Borel setting. More specifically, we prove that any standard Borel group can be realized as the Borel automorphism group of a Borel graph. A slight modification of our construction also yields the following result in topological setting: Any Polish group can be realized as the homeomorphic ...
Onur Bilge, Burak Kaya
openaire   +3 more sources

Integral Menger Curvature and Rectifiability of n-dimensional Borel sets in Euclidean N-space [PDF]

, 2015
In this work we show that an $n$-dimensional Borel set in Euclidean $N$-space with finite integral Menger curvature is $n$-rectifiable, meaning that it can be covered by countably many images of Lipschitz continuous functions up to a null set in the ...
M. Meurer
semanticscholar   +1 more source

Concentration inequalities for $s$-concave measures of dilations of Borel sets and applications [PDF]

, 2008
We prove a sharp inequality conjectured by Bobkov on the measure of dilations of Borel sets in the Euclidean space by a $s$-concave probability measure.
M. Fradelizi
semanticscholar   +1 more source

Turning Borel sets into clopen sets effectively [PDF]

, 2012
We present the effective version of the theorem about turning Borel sets in Polish spaces into clopen sets while preserving the Borel structure of the underlying space.
Vassilios Gregoriades
semanticscholar   +1 more source