zbMATH — the first resource for mathematics

The Brooks-Jewett theorem for \(k\)-triangular functions on difference posets and orthoalgebras. (English) Zbl 0961.28003
Summary: We introduce \(k\)-triangular functions on difference posets and we prove a Brooks-Jewett-type theorem for such functions that are defined on a difference poset (or an effect algebra) satisfying the weak subsequential interpolation property. This result enables us to obtain the previously known Brooks-Jewett theorems for orthoalgebras and orthomodular lattices.

28A60 Measures on Boolean rings, measure algebras
28B05 Vector-valued set functions, measures and integrals
06C15 Complemented lattices, orthocomplemented lattices and posets
Full Text: EuDML
[1] BIRKHOFF G., von NEUMANN J.: The logic of quantum mechanics. Ann. of Math. 37 (1936), 823-843. · Zbl 0015.14603
[2] D’ANDREA A. B., De LUCIA P.: The Brooks-Jewett theorem on an orthomodular lattice. J. Math. Anal. Appl. 154 (1991), 507-522. · Zbl 0727.28008
[3] DVUREČENSKIJ A., RIEČAN B.: Decomposition of measures on orthoalgebras and difference posets. Internat. J. Theoret. Phys. 33 (1994), 1387-1402. · Zbl 0815.03038
[4] FOULIS D. J., GREECHIE R. J., RÜTTIMANN G. T.: Filters and supports. Internat. J. Theoret. Phys. 31 (1992), 789-807. · Zbl 0764.03026
[5] FOULIS D. J., BENNETT M. K.: Effect algebras and unsharp quantum logics. Found. Phys. 24 (1994), 1325-1346. · Zbl 1213.06004
[6] FRENICHE F. J.: The Vitali-Hahn-Saks theorem for Boolean algebras with the subsequential interpolation property. Proc. Amer. Math. Soc. 92 (1984), 362-366. · Zbl 0529.28004
[7] GUARIGLIA E.: K-triangular functions on an orthomodular lattice and the Brooks-Jewett theorem. Rad. Mat. 6 (1990), 241-251. · Zbl 0763.28006
[8] GUDDER S. P.: Quantum Probability. Academic Press, Boston, 1988. · Zbl 0653.60004
[9] HABIL E. D.: Brooks-Jewett and Nikodym convergence theorems for orthoalgebras that have the weak subsequential interpolation property. Intern. J. Theoret. Phys. 34 (1995), 465-491. · Zbl 0822.60004
[10] HABIL E. D.: Morphisms and pasting of orthoalgebras. Math. Slovaca 47 (1997), 405-416. · Zbl 1057.81005
[11] HABIL E. D.: Orthosummable orthoalgebras. Intern. J. Theoret. Phys. 33 (1994), 1957-1984. · Zbl 0818.03030
[12] KALMBACH G.: Orthomodular Lattices. Academic Press, London-New York, 1983. · Zbl 0528.06012
[13] KOPKA F.-CHOVANEC F.: D-posets. Math. Slovaca 44 (1994), 21-34. · Zbl 0789.03048
[14] NAVARA M.-PTÁK P.: Difference posets and orthoalgebras. BUSEFAL 69 (1997),64-69.
[15] PAGE W.: Topological Uniform Structures. Wiley, New York, 1978. · Zbl 0397.46001
[16] PAP E.: The Vitali-Hahn-Saks theorems for k-triangular set functions. Atti. Sem. Mat. Fis. Univ. Modena 25 (1987), 21-32. · Zbl 0626.28001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.