Lattice-valued Borel measures. II

Author:
Surjit Singh Khurana

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

MSC:
Primary 28A55

MathSciNet review:
0460590

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let *T* be a completely regular Hausdorff space, the set of all bounded real-valued continuous functions on *T, E* a boundedly monotone complete ordered vector space, and a positive linear map. It is proved that under certain conditions there exist -additive, -smooth or tight *E*-valued measures on *T* which represent .

**[1]**Samuel Kaplan,*On the second dual of the space of continuous functions*, Trans. Amer. Math. Soc.**86**(1957), 70–90. MR**0090774**, 10.1090/S0002-9947-1957-0090774-3**[2]**S. S. Khurana,*Lattice-valued Borel measures*, Rocky Mountain J. Math.**6**(1976), no. 2, 377–382. MR**0399409****[3]**V. S. Varadarajan,*Measures on topological spaces*, Mat. Sb. (N.S.)**55 (97)**(1961), 35–100 (Russian). MR**0148838****[4]**J. D. Maitland Wright,*Stone-algebra-valued measures and integrals*, Proc. London Math. Soc. (3)**19**(1969), 107–122. MR**0240276****[5]**J. D. Maitland Wright,*Measures with values in a partially ordered vector space*, Proc. London Math. Soc. (3)**25**(1972), 675–688. MR**0344413****[6]**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**0330411****[7]**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**0333116****[8]**J. D. Maitland Wright,*An extension theorem*, J. London Math. Soc. (2)**7**(1974), 531–539. MR**0344414****[9]**J. D. Maitland Wright,*Embeddings in vector lattices*, J. London Math. Soc. (2)**8**(1974), 699–706. MR**0352953**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
28A55

Retrieve articles in all journals with MSC: 28A55

Additional Information

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

Keywords:
-smooth measures,
tight measures,
weakly -distributive lattices,
monotone order -continuous,
order -continuous,
monotone order -closed,
order -closed

Article copyright:
© Copyright 1978
American Mathematical Society