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Cupping with random sets
Cupping random sets Logic
2012/6/29
We prove that a set is K-trivial if and only if it is not weakly ML-cuppable. Further, we show that a set below zero jump is K-trivial if and only if it is not ML-cuppable. These results settle a ques...
We develop a new technique that allows us to show in a unified way that many well-known combinatorial theorems, including Tur\'an's theorem, Szemer\'edi's theorem and Ramsey's theorem, hold almost su...
The Distribution of Unbounded Random Sets and the Multivalued Strong Law of Large Numbers in Nonreflexive Banach Spaces
distribution of random sets multivalued strong law of large numbers set convergence measurable multifunctions convex sets
2009/1/20
In the first part, we introduce appropriate tools concerning the distribution of random sets. We study the relation between the distribution of a random set, whose values are closed subsets of a Banac...
From random sets to continuous tensor products: answers to three questions of W. Arveson
continuous tensor products W. Arveson
2010/10/29
The set of zeros of a Brownian motion gives rise to a product system in the sense of William Arveson (that is, a continuous tensor product system of Hilbert spaces). Replacing the Brownian motion with...