Jordan Algebras of Abstract Measurable Operators for JBW-Algebras

We study measurable and locally measurable operators for JBW-algebras. These concepts are described abstractly, i.e., their definitions do not involve the notion of an unbounded operator. We establish that these operators form a Jordan analog of a Baer $*$-algebra and describe the relationship between abstract measurable operators for the Jordan algebras and those for their realizations in a Boolean-valued model of set theory.