Invariant Measures and Radon-Nikodym Derivatives

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...

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...

Reasonable non–Radon–Nikodym idealss

For any abelian Polish σ-compact group H there exist an Fσ ideal Z ⊆ P (N) and a Borel Z -approximate homomorphism f : H → HN which is not Z -approximable by a continuous true homomorphism g : H → HN .

A Radon-Nikodym approach to measure information