Bull. Austral. Math. Soc. 72(2) pp.291--298, 2005.

# Bounded vector measures on effect algebras

### Hunnam Kim

This paper was supported by Kumoh National Institute of Technology.

## Abstract

Let (L,, , 0, 1) be an effect algebra and X a locally convex space with dual X. A function : L X is called a measure if (a b) = (a) + (b) whenever ab in L and it is bounded if (an) is bounded for each orthogonal sequence {an} in L. We establish five useful conditions that are equivalent to boundedness for vector measures on effect algebras.

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## References

1. S.P. Gudder;
Quantum probability (Academic Press, Boston, 1989). MR958911
2. E.D. Habil;
Brooks-Jewett and Nikodym convergence theorems for orthoalgebras that have the weak subsequential interpolation property,
Internat. J. Theoret. Phys. 34 (1994), pp. 465--491. MR1330347
3. R.L. Li, R.C. Cui and M.H. Zhao;
Invariants on all admissible polar topologies,
Chinese Ann. Math. Ser. A 19 (1998), pp. 289--294. MR1641098
4. R. Li and S.M. Kang;
Characterizations of bounded vector measures,
Bull. Korean Math. Soc. 37 (2000), pp. 209--215. MR1757488
5. R.L. Li and Q.Y. Bu;
Locally convex spaces containing no copy of c0,
J. Math. Anal. Appl. 172 (1993), pp. 205--211. MR1199505
6. F.G Mazario;
Convergence theorems for topological group valued measures en effect algebras,
Bull. Austral. Math. Soc. 64 (2001), pp. 213--231. MR1860059
7. C. Swartz and C. Stuart;
Orlicz-Pettis theorems for multiplier convergent series,
Z. Anal. Anwendungen 17 (1998), pp. 805--811. MR1669893
8. A. Wilansky;
Modern methods in topological vector spaces (McGraw-Hill, New York, 1978). MR518316

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