Bulletin of the Australian Mathematical Society Bull. Austral. Math. Soc. 0004-9727 ALNBAB 2005 72 2 10.wxyz/CV72P2 http://www.austms.org.au/Publ/Bulletin/V72P2/ Hong Taek Hwang Longlu Li Hunnam Kim 14 February 2006 2006 2 14 291 298 722-5136-HwLiKim-2005 10.wxyz/C2005V72P2p291 http://www.austms.org.au/Publ/Bulletin/V72P2/722-5136-HwLiKim/ Let $(L, \bot , \oplus , 0, 1)$ be an effect algebra and $X$ a locally convex space with dual $X^{\prime }$. A function $\mu : L \rightarrow X$ is called a measure if $\mu (a \oplus b) = \mu (a) + \mu (b)$ whenever $a \bot b$ in $L$ and it is bounded if $\bigl \{\mu (a_n) \bigr \}_{n=1}^{\infty }$ is bounded for each orthogonal sequence $\{a_n \}$ in $L$. We establish five useful conditions that are equivalent to boundedness for vector measures on effect algebras. 28B10, 03G12, 46L51, 81P10 MR2183410 02246391 This paper was supported by Kumoh National Institute of Technology S.P. Gudder Academic Press MR958911 S.P. Gudder; \textit{Quantum probability} (Academic Press, Boston, 1989). E.D. Habil Internat. J. Theoret. Phys. MR1330347 E.D. Habil; Brooks-Jewett and Nikodym convergence theorems for orthoalgebras that have the weak subsequential interpolation property, \textit{Internat. J. Theoret. Phys.} \textbf{34} (1994), pp.~465--491. R.L. Li, R.C. Cui and M.H. Zhao Chinese Ann. Math. Ser. A MR1641098 R.L. Li, R.C. Cui and M.H. Zhao; Invariants on all admissible polar topologies, \textit{Chinese Ann. Math. Ser. A} \textbf{19} (1998), pp.~289--294. R. Li and S.M. Kang Bull. Korean Math. Soc. MR1757488 R. Li and S.M. Kang; Characterizations of bounded vector measures, \textit{Bull. Korean Math. Soc.} \textbf{37} (2000), pp.~209--215. R.L. Li and Q.Y. Bu J. Math. Anal. Appl. MR1199505 R.L. Li and Q.Y. Bu; Locally convex spaces containing no copy of $c0$, \textit{J. Math. Anal. Appl.} \textbf{172} (1993), pp.~205--211. F.G Mazario Bull. Austral. Math. Soc. MR1860059 F.G Mazario; Convergence theorems for topological group valued measures en effect algebras, \textit{Bull. Austral. Math. Soc.} \textbf{64} (2001), pp.~213--231. C. Swartz and C. Stuart Z. Anal. Anwendungen MR1669893 C. Swartz and C. Stuart; Orlicz-Pettis theorems for multiplier convergent series, \textit{Z. Anal. Anwendungen} \textbf{17} (1998), pp.~805--811. A. Wilansky McGraw-Hill MR518316 A. Wilansky; \textit{Modern methods in topological vector spaces} (McGraw-Hill, New York, 1978).