As a consequence of the extreme precision of the measurements it performs, a LIGO/VIRGO-type interferometric gravitational wave detector (IGWD) is a macroscopic apparatus for which quantum effects are not negligible. We observe that this property of IGWDs can be exploited to probe some aspects of the interface between Quantum Mechanics and Gravity. In particular, we find that IGWDs can test two...

In 1998, it was proved by Ben-David and Litman that a concept space has a sample compression scheme of size d if and only if every finite subspace has a sample compression scheme of size d. In the compactness theorem, measurability of the hypotheses of the created sample compression scheme is not guaranteed; at the same time measurability of the hypotheses is a necessary condition for learnabil...

The probabilistic type spaces in the sense of Harsanyi [Management Sci. 14 (1967/68) 159–182, 320–334, 486–502] are the prevalent models used to describe interactive uncertainty. In this paper we examine the existence of a universal type space when beliefs are described by finitely additive probability measures. We find that in the category of all type spaces that satisfy certain measurability ...

A general parameter process defined by a continuum of random variables is not jointly measurable with respect to the usual product σ-algebra. For the case of independent random variables, a one-way Fubini extension of the product space was constructed in [11] to satisfy a limited form of joint measurability. For the general case we show that this extension exists if and only if there is a count...