We discuss the relationships between effect algebras with the Riesz Decomposition Property and partially ordered groups with interpolation. We show that any σ-orthocomplete atomic effect algebra with the Riesz Decomposition Property is an MV-effect algebras, and we apply this result for pseudo-effect algebras and for states.

In this paper, the properties of the super quantum measures are studied. Firstly, the products of Dirac measures are discussed; Secondly, based on the properties of Dirac measures, the structures of super quantum measures are characterized; At last, we prove that any super quantum measure can determine a unique diagonally positive strongly symmetric signed measure. This result verifies the conjecture which was proposed by Gudder.

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 $\lambda$ on the tensor product $E\otimes E$ can determine a quantum measure $\mu$ on a finite effect algebra $E$ with the RDP such that \(\mu (...) (x)=\lambda (x\otimes x)\) for any $x\in E$ . Furthermore, some conditions for a grade-2 additive measure $\mu$ on a finite effect algebra $E$ are provided to guarantee that there exists a unique diagonally positive symmetric signed measure $\lambda$ on $E\otimes E$ such that $\mu (x)=\lambda (x\otimes x)$ for any $x\in E$ . At last, it is showed that any grade- $t$ quantum measure on a finite effect algebra $E$ with the RDP is essentially established by the values on a subset of $E$. (shrink)