A multivariate generalization of a theorem of R. H. Farrell

Author:
D. Plachky

Journal:
Proc. Amer. Math. Soc. **113** (1991), 163-165

MSC:
Primary 28A60; Secondary 28A25

DOI:
https://doi.org/10.1090/S0002-9939-1991-1052873-4

MathSciNet review:
1052873

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Abstract: Let denote a finite measure space and -measurable functions, . Then the algebra of functions generated by is a dense subset of if and only if for any there exists some , such that is valid. In particular, this condition is satisfied if is a Blackwell space and is in addition one-to-one.

**[1]**R. G. Douglas,*On extremal measures and subspace density*, II, Proc. Amer. Math. Soc.**17**(1966), 1363-1365. MR**0205053 (34:4888)****[2]**R. H. Farrell,*Dense algebras of functions in*, Proc. Amer. Math. Soc.**13**(1962), 324-328. MR**0142009 (25:5404)****[3]**P. A. Meyer,*Probability and potentials*, Blaisdell, Waltham, MA, 1966. MR**0205288 (34:5119)****[4]**D. Plachky,*Extremal and monogenic additive set functions*, Proc. Amer. Math. Soc.**54**(1976), 193-196. MR**0419711 (54:7729)****[5]**M. M. Rao,*Measure theory and integration*, Wiley, New York, 1987. MR**891879 (89k:28001)**

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DOI:
https://doi.org/10.1090/S0002-9939-1991-1052873-4

Article copyright:
© Copyright 1991
American Mathematical Society