Abstract
Let X be a Hausdorff space and let L be a sublattice of the vector lattice of real continuous functions on X. Consider a localizable Daniell integral μ on L, i.e. one which is defined by a Radon measure m on X by the formula μ(φ)=∫φdm. Then if G is a group of homeomorphisms of X leaving L invariant, it is shown that under appropriate hypotheses, the invariance of μ under the action of G implies the quasi-invariance of a certain class of measures associated with m on a quotient space Y of X. Conversely, if G is locally compact and Y=G/H, the class of quasi-invariant Radon measures on Y is associated in this way to a G-invariant Daniell integral on a certain half-line bundle over Y.
Keywords
- Radon Measure
- Hausdorff Space
- Measurable Selection
- Continuous Section
- Invariant Section
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References
N. Bourbaki, Intégration ch.7, Hermann.
E.G.F. Thomas and A. Volčič, Daniell integrals represented by Radon measures, in preparation.
E.G.F. Thomas, Integral representation in Convex cones. Report, University of Groningen ZW 7703, 1977.
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© 1984 Springer-Verlag
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Thomas, E.G.F. (1984). Invariant Daniell integrals. In: Kölzow, D., Maharam-Stone, D. (eds) Measure Theory Oberwolfach 1983. Lecture Notes in Mathematics, vol 1089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072610
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DOI: https://doi.org/10.1007/BFb0072610
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Print ISBN: 978-3-540-13874-7
Online ISBN: 978-3-540-39069-5
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