Accessible cylindrical measure and Bochner's theorem

XBarnacle: Making Theorem Provers More Accessible

XBarnacle was built to meet the challenge of incorporating interactive features in the automated theorem prover CLAM whilst preserving the advantages of automation. Many people are not able to use theorem provers to their full strength. The aim of our research is to make semi-automated theorem proving a real possibility for a wide range of people – from those primarily interested in formal spec...

Wiener measure and Donsker’s theorem

Stable Ramsey's Theorem and Measure

The stable Ramsey’s theorem for pairs has been the subject of numerous investigations in mathematical logic. We introduce a weaker form of it by restricting from the class of all stable colorings to subclasses of it that are non-null in a certain effective measure-theoretic sense. We show that the sets that can compute infinite homogeneous sets for non-null many computable stable colorings and ...

Invariant Measure, the Recurrence Theorem, and the Ergodic Theorem

converge a.e. to a finite limit, where fs is the characteristic function of the set E. G. D. Birkhoff's Ergodic Theorem asserts this conclusion if T is measure-preserving, in the sense that m(T~1E)=m(E) for each measurable set E. The same conclusion can be asserted under somewhat more general circumstances. We shall say that T admits a finite, equivalent, invariant measure if there is a finite ...

An Upward Measure Separation Theorem

It is shown that almost every language in ESPACE is very hard to approximate with circuits It follows that P BPP implies that E is a measure subset of ESPACE