Equivalence and Radon-Nikodym derivatives of Gaussian measures

Radon–Nikodym derivatives of quantum operations

Given a completely positive ~CP! map T, there is a theorem of the Radon– Nikodym type @W. B. Arveson, Acta Math. 123, 141 ~1969!; V. P. Belavkin and P. Staszewski, Rep. Math. Phys. 24, 49 ~1986!# that completely characterizes all CP maps S such that T2S is also a CP map. This theorem is reviewed, and several alternative formulations are given along the way. We then use the Radon–Nikodym formali...

The Radon-Nikodym problem for approximately proper equivalence relations

We study the Radon-Nikodym problem for approximately proper equivalence relations and more specifically the uniqueness of certain Gibbs states. One of our tools is a variant of the dimension group introduced in the study of AF algebras. As applications, we retrieve sufficient conditions for the uniqueness of traces on AF algebras and parts of the PerronFrobenius-Ruelle theorem.

The Radon-Nikodym problem for approximately proper equivalence relations

On the Connection between the Hilger and Radon–Nikodym Derivatives

We show that the Hilger derivative on time scales is a special case of the Radon–Nikodym derivative with respect to the natural measure associated with every time scale. Moreover, we show that the concept of delta absolute continuity agrees with the one from measure theory in this context.

A Radon-nikodym Theorem for Stone Algebra Valued Measures

Introduction. Let C(S) be the ring of continuous real valued functions on a compact Hausdorff space S. Stone [5] shows that each bounded subset of C(S) has a least upper bound (in C(S)) if and only if the closure of each open subset of S is open ; in this event we call C(S) a Stone algebra. Throughout this paper C(S) is a Stone algebra. It is convenient to adjoin an object +00, not in C(S), and...