A note on liftings of linear continuous functionals

Author:
Horst Osswald

Journal:
Proc. Amer. Math. Soc. **120** (1994), 453-456

MSC:
Primary 03H05; Secondary 28E05, 46S20

DOI:
https://doi.org/10.1090/S0002-9939-1994-1165064-6

MathSciNet review:
1165064

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that for each bounded Loeb space a functional has a lifting if and only if . If , then every has a lifting.

**[1]**S. Albeverlo, J. E. Fenstad, R. Høegh Krohn, and T. L. Lindstrøm,*Nonstandard method in stochastic analysis and mathematical physics*, Academic Press, New York, 1986. MR**859372 (88f:03061)****[2]**R. A. Anderson,*A nonstandard representation of Brownian motion and Ito-integration*, Israel J. Math.**15**(1976).**[3]**E. Hewitt and K. Stromberg,*Real and abstract analysis*, Springer-Verlag, New York, 1969. MR**0367121 (51:3363)****[4]**D. H. Hoover and E. A. Perkins,*Nonstandard construction of the stochastic integral and applications to stochastic differential equations*. I, II, Trans. Amer. Math. Soc.**275**(1983), 1-36, 37-58. MR**678335 (85d:60111)****[5]**A. E. Hurd and P. A. Loeb,*An introduction to nonstandard real analysis*, Academic Press, New York, 1985. MR**806135 (87d:03184)****[6]**H. J. Keisler,*An infinitesimal approach to stochastic analysis*, Mem. Amer. Math. Soc., no. 297, Amer. Math. Soc., Providence, RI, 1984. MR**732752 (86c:60086)****[7]**T. L. Lindstrøm,*Hyperfinite stochastic integration*. I, II, III, and addendum, Math. Scand.**46**(1980).**[8]**P. A. Loeb,*Conversion from nonstandard to standard measure spaces and applications to probability theory*, Trans. Amer. Math. Soc.**211**(1975), 113-122. MR**0390154 (52:10980)****[9]**-,*A functional approach to nonstandard measure theory*, Contemp. Math., vol. 26, Amer. Math. Soc., Providence, RI, 1984, pp. 251-261. MR**737406 (86b:28026)****[10]**H. Osswald,*Vector-valued Loeb measures and the Lewis integral*, Math. Scand**68**(1991). MR**1129592 (93m:28024)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
03H05,
28E05,
46S20

Retrieve articles in all journals with MSC: 03H05, 28E05, 46S20

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1165064-6

Article copyright:
© Copyright 1994
American Mathematical Society