Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Commuting and topological densities and liftings


Author: Trevor J. McMinn
Journal: Trans. Amer. Math. Soc. 211 (1975), 1-22
MSC: Primary 28A15; Secondary 46G15
DOI: https://doi.org/10.1090/S0002-9947-1975-0432845-6
MathSciNet review: 0432845
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For fairly general conditions on a measure space, a group of bijections on the space and a topology on the space, densities and lifttings commuting with members of the group and with topologies finer than the given topology are obtained.


References [Enhancements On Off] (What's this?)

  • [1] K. Bichteler, On the strong lifting property, Illinois J. Math. 16 (1972), 370-380. MR 45 #5311. MR 0296250 (45:5311)
  • [2] -, An existence theorem for strong liftings, J. Math. Anal. Appl. 33 (1971), 20-22. MR 42 #4700. MR 0269805 (42:4700)
  • [3] -, A reduction of the strong lifting problem, Invent. Math. 11 (1970), 159-162. MR 44 #2906. MR 0285688 (44:2906)
  • [4] J. Dugundji, Topology, Allyn and Bacon, Boston, Mass., 1966, 9.1 Theorem (J. Nagata and Yu. M. Smirnov), pp. 193-194. MR 33 #1824. MR 0193606 (33:1824)
  • [5] P. A. Fillmore, On the topology induced by measure, Proc. Amer. Math. Soc. 17 (1966), 854-857. MR 33 #5830. MR 0197667 (33:5830)
  • [6] J. Gapaillard, Relèvements sur une algèbre de parties d'un ensemble, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A1798-A1800. MR 45 #7014. MR 0297962 (45:7014)
  • [7] A. Ionescu-Tulcea and C. Ionescu-Tulcea, Topics in the theory of lifting, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 48, Springer-Verlag, New York, 1969. MR 43 #2185. MR 0276438 (43:2185)
  • [8] -, Liftings for abstract valued functions and separable stochastic processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 13 (1969), 114-118. MR 43 #2763. MR 0277026 (43:2763)
  • [9] C. Ionescu-Tulcea, On liftings and derivation bases, J. Math. Anal. Appl. 35 (1971), 449-466. MR 43 #7583. MR 0281869 (43:7583)
  • [10] -, Liftings for functions with values in a completely regular space, Math. Ann. 187 (1970), 200-206. MR 42 #1973. MR 0267071 (42:1973)
  • [11] -, On the lifting property and disintegration of measures, Bull. Amer. Math. Soc. 71 (1965), 829-842. MR 34 #600. MR 0200712 (34:600)
  • [12] H. Kenyon and A. P. Morse, Runs, Pacific J. Math. 8 (1958), 811-824. MR 21 #2967. MR 0104210 (21:2967)
  • [13] D. Maharam, On a theorem of von Neumann, Proc. Amer. Math. Soc. 9 (1958), 987-994. MR 21 #4220. MR 0105479 (21:4220)
  • [14] R. Maher, A note on strong liftings, J. Math. Anal. Appl. 29 (1970), 633-639. MR 43 #7584. MR 0281870 (43:7584)
  • [15] A. P. Morse, The role of internal families in measure theory, Bull. Amer. Math. Soc. 50 (1944), 723-728. MR 6, 120. MR 0011107 (6:120c)
  • [16] J. von Neumann, Algebräsche Repräsentanten der Funktionen bis auf eine Menge von Masse null, J. Reine Angew. Math. 165 (1931), 109-115.
  • [17] M. Sion, A theory of semigroup valued measures, Springer-Verlag, New York, 1973, Appendix. MR 0450503 (56:8797)
  • [18] -, Introduction to the methods of real analysis, Holt, Rinehart and Winston, New York, 1968. MR 37 #5332. MR 0229758 (37:5332)
  • [19] T. Traynor, An elementary proof of the lifting theorem, Pacific J. Math. 53 (1974), 267-272. MR 0367659 (51:3901)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28A15, 46G15

Retrieve articles in all journals with MSC: 28A15, 46G15


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0432845-6
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society