We consider positive operator-valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator-valued measure seen in the quantum information theory literature. We consider integrals of quantum random variables, extending work done by Farenick--Plosker--Smith (2011) to the setting of infinite-dimensional Hilbert space, and develop positive operator-valued versions of a number of classical measure decomposition theorems. This is joint work with D. Mclaren and C. Ramsey.

I will explain further details about the talk one week before, in particular on Tingley's problem for operator algebras.