MV-Observables and MV-Algebras

We introduce MV-observables, an analogue of observables for MV-algebras, as -homomorphisms from the Borel tribe generated by the Borel sets of and constant functions from 0, 1 into an MV-algebra M. We show that it is possible to define such observables only for weakly divisible MV-algebras. We present a representation as well as a so-called calculus of MV-observables, which enables us to construct, e.g., the sum or product of MV-observables