Quantum Measures on Finite Effect Algebras with the Riesz Decomposition Properties

One kind of generalized measures called quantum measures on finite effect algebras, which fulfil the grade-2 additive sum rule, is considered. One basis of vector space of quantum measures on a finite effect algebra with the Riesz decomposition property (RDP for short) is given. It is proved that any diagonally positive symmetric signed measure on the tensor product can determine a quantum measure on a finite effect algebra with the RDP such that for any . Furthermore, some conditions for a grade-2 additive measure on a finite effect algebra are provided to guarantee that there exists a unique diagonally positive symmetric signed measure on such that for any . At last, it is showed that any grade- quantum measure on a finite effect algebra with the RDP is essentially established by the values on a subset of .