|
HYPERFINITE TRANSVERSAL THEORY. II
Author(s):
Bosko
Zivaljevic
Journal:
Trans. Amer. Math. Soc.
348
(1996),
1921-1938.
MSC (1991):
Primary 03H04, 03E15;
Secondary 04A15, 05C99, 28E05, 54H05
MathSciNet review:
1348159
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We continue the investigation of validity of Hall's theorem in the case of the Loeb space of an internal, uniformly distributed, hyperfinite measure space initiated in1992 by the author. Some new classes of graphs are introduced for which the measure theoretic version of Hall's theorem still holds.
References:
- [Ar]
- Z. Artstein, Distributions of Random Sets and Random Selections, Israel Journal of Math. 46 (1983), 313-324. MR 85m:60017
- [Be]
- E. Bertossi, Standard Capacities With Nonstandard Pavings, Notas De LA Sociedad De Mat. De Chile V (1986), 1-6. MR 88c:26023
- [BoVa]
- B. Bollobas and N. Th. Varopoulos, Representation of Systems of Measurable Sets, Math.Proc.Camb.Phil.Soc. 78 (1974), 323-325. MR 52:686
- [BrSi]
- D. W. Bressler and M. Sion, The Current Theory of Analytic Sets, Can.J.Math. 16 (1964), 207-230. MR 29:1153
- [Ha]
- P. Hall, On Representatives of Subsets, J. London Math. Soc. 10 (1935), 26-30.
- [He]
- C. W. Henson, Analytic Sets, Baire Sets, and the Standard Part Map, Canadian J. Math. 31 (1979), 663-672. MR 80i:28019
- [HeRo]
- C. W. Henson and D. Ross, Analytic mappings on hyperfinite sets, Proc.Amer.Math.Soc. 2 (1993), 587-596. MR 93g:03055
- [HuLo]
- A. E. Hurd and P. A. Loeb, An Introduction to Nonstandard Real Analysis, Academic Press, New York, 1985. MR 87d:03184
- [KKLM]
- H. J. Keisler, K. Kunen, A. Miller and S. Leth, Descriptive Set Theory over Hyperfinite sets, J. Symbolic Logic 54 (4) (1989), 1167-1180. MR 91c:03040
- [Lo]
- P. A. Loeb, Conversion from Nonstandard to Standard Measure Space and Applications in Probability Theory, Trans.Amer.Math.Soc. 211 (1975), 113-122. MR 52:10980
- [Ma]
- Mauldin, D., One-to-one Selections-marriage Theorems, American Journal of Mathematics 104 (1982), 823-828. MR 84b:28013
- [Me]
- P. A. Meyer, Probabilités et Potentiel, Hermann, Paris, 1966. MR 34:5118
- [NW]
- C. Nash-Williams, Unexplored and Semi-Explored Territories in Graph Theory, New Directions in Graph Theory (Frank Harray, ed.), Academic Press, 1973. MR 52:7944
- [Ro]
- D. Ross, Lifting Theorems in Nonstandard Measure Theory, Proc.Amer.Math.Soc 109 (1990), 809-822. MR 91b:03110
- [SchZi]
- K. Schilling and B. \v{Z}ivaljevi\'{c}, Louveau's Theorem for the Descriptive Set Theory of Internal Sets, (submitted).
- [StBa]
- K. D. Stroyan, J. M. Bayod, Foundations of Infinitesimal Stochastic Analysis, North-Holland, Amsterdam, 1986. MR 87m:60001
- [Zi1]
- B. \v{Z}ivaljevi\'{c}, Hyperfinite Transversal Theory, Trans. Amer. Math. Soc 330 (1992), 371-399. MR 92f:03073
- [Zi2]
- ------, Rado's Theorem for the Loeb Space of an internal
-finitely additive measure space, Proc. Amer. Math. Soc. 112 (1991), 203-207. MR 91h:03092 - [Zi3]
- ------, The structure of graphs all of whose
sections are internal sets, J. of Symbolic Logic 56 (1991), 50-66. MR 92j:03059 - [Zi4]
- ------, Graphs with
sections, Arch. Math. Logic 32 No.4 (1993), 259-273. MR 94e:03065 - [Zi5]
- ------,
functions are almost internal, Trans. Amer. Math. Soc. 347 (1995), 2621--2632. - [Zi6]
- ------,
sets of infinite Loeb measure, Proc. Amer. Math. Soc. (to appear).
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (1991):
03H04, 03E15,
04A15, 05C99, 28E05, 54H05
Retrieve articles in all Journals with
MSC (1991):
03H04, 03E15,
04A15, 05C99, 28E05, 54H05
Additional Information:
Bosko
Zivaljevic
Affiliation:
Department of Computer Science, The University of Illinois at Urbana - Champaign, Urbana, Illinois 61801
Address at time of publication:
International Paper Company, Process Management Computer, 3101 International Drive East, Mobile, Alabama 36606
Email:
zivaljev@cs.uiuc.edu
DOI:
10.1090/S0002-9947-96-01596-6
PII:
S 0002-9947(96)01596-6
Keywords:
Nonstandard measure theory,
transversal theory,
Hall's theorem,
descriptive set theory of internal sets
Received by editor(s):
August 7, 1994
Received by editor(s) in revised form:
June 5, 1995
Copyright of article:
Copyright
1996,
American Mathematical Society
|