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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...
It is shown that every random closed set X in Rd, taking its realizations in the extended convex ring, is (up to equivalence) the union set of a po'int process Y of convex particles with the same i...
A random set analogue of the Snell problem is presented. In the original Snell's problem one observes a sequence of random variables (t,), say a gambler's capital at successive games. If the gambler...
We study random convex compact sets infinitely divisible with respect to the Minkowski addition and establish a sufficient condition for their association as well as a necessary and sufficient condi...
Shape estimation and object reconstruction are common problems in image analysis. Mathematically,viewing objects in the image plane as random sets reduces the problem of shape estimation to inference ...
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...
The QQ plot is a commonly used technique for informally deciding whether a univariate random sample of size n comes from a specified distribution F. The QQ plot graphs the sample quantiles against th...
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...

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