Sequential convergence in the order duals of certain classes of Riesz spaces

Dodds, P. G.

doi:10.1090/S0002-9947-1975-0358282-0

Sequential convergence in the order duals of certain classes of Riesz spaces
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by P. G. Dodds

Trans. Amer. Math. Soc. 203 (1975), 391-403

DOI: https://doi.org/10.1090/S0002-9947-1975-0358282-0

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Abstract:

Several results of Hahn-Vitali-Saks type are given for sequences in the order dual of an Archimedean Riesz space with separating order dual. The class of Riesz spaces considered contains those which are Dedekind $\sigma$-complete, or have the projection property or have an interpolation property introduced by G. L. Seever. The results depend on recent work of O. Burkinshaw and some results of uniform boundedness type.

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