Commuting and topological densities and liftings

McMinn, Trevor J.

doi:10.1090/S0002-9947-1975-0432845-6

Commuting and topological densities and liftings
HTML articles powered by AMS MathViewer

by Trevor J. McMinn

Trans. Amer. Math. Soc. 211 (1975), 1-22

DOI: https://doi.org/10.1090/S0002-9947-1975-0432845-6

PDF | Request permission

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

Klaus Bichteler, On the strong lifting property, Illinois J. Math. 16 (1972), 370–380. MR 296250
Klaus Bichteler, An existence theorem for strong liftings, J. Math. Anal. Appl. 33 (1971), 20–22. MR 269805, DOI 10.1016/0022-247X(71)90177-6
Klaus Bichteler, A reduction of the strong lifting problem, Invent. Math. 11 (1970), 159–162. MR 285688, DOI 10.1007/BF01404609
James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
P. A. Fillmore, On topology induced by measure, Proc. Amer. Math. Soc. 17 (1966), 854–857. MR 197667, DOI 10.1090/S0002-9939-1966-0197667-2
Jacques Gapaillard, Relèvements sur une algèbre de parties d’un ensemble, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A1798–A1800 (French). MR 297962
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, Inc., New York, 1969. MR 0276438, DOI 10.1007/978-3-642-88507-5
A. Ionescu Tulcea and C. Ionescu Tulcea, Liftings for abstract valued functions and separable stochastic processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 13 (1969), 114–118. MR 277026, DOI 10.1007/BF00537015
C. Ionescu Tulcea, On liftings and derivation bases, J. Math. Anal. Appl. 35 (1971), 449–466. MR 281869, DOI 10.1016/0022-247X(71)90229-0
C. Ionescu Tulcea, Liftings for functions with values in a completely regular space, Math. Ann. 187 (1970), 200–206. MR 267071, DOI 10.1007/BF01432253
C. Ionescu Tulcea, On the lifting property and disintegration of measures, Bull. Amer. Math. Soc. 71 (1965), 829–842. MR 200712, DOI 10.1090/S0002-9904-1965-11407-0
H. Kenyon and A. P. Morse, Runs, Pacific J. Math. 8 (1958), 811–824. MR 104210, DOI 10.2140/pjm.1958.8.811
Dorothy Maharam, On a theorem of von Neumann, Proc. Amer. Math. Soc. 9 (1958), 987–994. MR 105479, DOI 10.1090/S0002-9939-1958-0105479-6
R. Maher, A note on strong liftings, J. Math. Anal. Appl. 29 (1970), 633–639. MR 281870, DOI 10.1016/0022-247X(70)90071-5
Anthony P. Morse, The role of internal families in measure theory, Bull. Amer. Math. Soc. 50 (1944), 723–728. MR 11107, DOI 10.1090/S0002-9904-1944-08223-2

Algebräsche Repräsentanten der Funktionen bis auf eine Menge von Masse null

165

Maurice Sion, A theory of semigroup valued measures, Lecture Notes in Mathematics, Vol. 355, Springer-Verlag, Berlin-New York, 1973. MR 0450503, DOI 10.1007/BFb0060133
Maurice Sion, Introduction to the methods of real analysis, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1968. MR 0229758
Tim Traynor, An elementary proof of the lifting theorem, Pacific J. Math. 53 (1974), 267–272. MR 367659, DOI 10.2140/pjm.1974.53.267