Lattice-valued Borel measures. II

Khurana, Surjit Singh

doi:10.1090/S0002-9947-1978-0460590-2

Lattice-valued Borel measures. II
HTML articles powered by AMS MathViewer

by Surjit Singh Khurana

Trans. Amer. Math. Soc. 235 (1978), 205-211

DOI: https://doi.org/10.1090/S0002-9947-1978-0460590-2

PDF | Request permission

Abstract:

Let T be a completely regular Hausdorff space, ${C_b}(T)$ the set of all bounded real-valued continuous functions on T, E a boundedly monotone complete ordered vector space, and $\varphi :{C_b}(T) \to E$ a positive linear map. It is proved that under certain conditions there exist $\sigma$-additive, $\tau$-smooth or tight E-valued measures on T which represent $\varphi$.

References

Samuel Kaplan, On the second dual of the space of continuous functions, Trans. Amer. Math. Soc. 86 (1957), 70–90. MR 90774, DOI 10.1090/S0002-9947-1957-0090774-3
S. S. Khurana, Lattice-valued Borel measures, Rocky Mountain J. Math. 6 (1976), no. 2, 377–382. MR 399409, DOI 10.1216/RMJ-1976-6-2-377
V. S. Varadarajan, Measures on topological spaces, Mat. Sb. (N.S.) 55 (97) (1961), 35–100 (Russian). MR 0148838
J. D. Maitland Wright, Stone-algebra-valued measures and integrals, Proc. London Math. Soc. (3) 19 (1969), 107–122. MR 240276, DOI 10.1112/plms/s3-19.1.107
J. D. Maitland Wright, Measures with values in a partially ordered vector space, Proc. London Math. Soc. (3) 25 (1972), 675–688. MR 344413, DOI 10.1112/plms/s3-25.4.675
J. D. Maitland Wright, The measure extension problem for vector lattices, Ann. Inst. Fourier (Grenoble) 21 (1971), no. 4, 65–85 (English, with French summary). MR 330411
J. D. Maitland Wright, An algebraic characterization of vector lattices with the Borel regularity property, J. London Math. Soc. (2) 7 (1973), 277–285. MR 333116, DOI 10.1112/jlms/s2-7.2.277
J. D. Maitland Wright, An extension theorem, J. London Math. Soc. (2) 7 (1974), 531–539. MR 344414, DOI 10.1112/jlms/s2-7.3.531
J. D. Maitland Wright, Embeddings in vector lattices, J. London Math. Soc. (2) 8 (1974), 699–706. MR 352953, DOI 10.1112/jlms/s2-8.4.699