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On dimensions of conformal repellers. Randomness and parameter dependency
Conditional measures and conditional expectation; Rohlin's Disintegration Theorem
1. | Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430, United States |
Sections 1 - 4 contain the statement and proof of Rohlin's Theorem. Sections 5 - 7 give a generalization of Rohlin's Theorem to the category of $\sigma$-finite measure spaces with absolutely continuous morphisms. Section 8 gives a less general but more powerful version of Rohlin's Theorem in the category of smooth measures on $C^1$ manifolds. Section 9 is an appendix which contains proofs of facts used throughout the paper.
References:
[1] |
H. Bergström, "Weak Convergence of Measures,'', Probability and Mathematical Statistics, (1982).
|
[2] |
D. Cohn, "Measure Theory,'', Reprint of the 1980 original, (1980).
|
[3] |
G. de Rham, "Differentiable Manifolds. Forms, Currents, Harmonic Forms,'', Translated from the French by F. R. Smith, 266 (1984).
|
[4] |
H. Federer, "Geometric Measure Theory,'', Die Grundlehren der mathematischen Wissenschaften, (1969).
|
[5] |
C. Hsiung, "A First Course in Differential Geometry,'', Pure and Applied Mathematics, (1981).
|
[6] |
D. Maharam, On the planar representation of a measurable subfield,, in, 1089 (1984), 47.
|
[7] |
V. Rohlin, On the fundamental ideas of measure theory,, Amer. Math. Soc. Translation, 1952 (1952).
|
[8] |
S. Srivastava, "A Course on Borel Sets,'', Graduate Texts in Mathematics, 180 (1998).
|
[9] |
S. Willard, "General Topology,'', Reprint of the 1970 original [Addison-Wesley, (1970).
|
show all references
References:
[1] |
H. Bergström, "Weak Convergence of Measures,'', Probability and Mathematical Statistics, (1982).
|
[2] |
D. Cohn, "Measure Theory,'', Reprint of the 1980 original, (1980).
|
[3] |
G. de Rham, "Differentiable Manifolds. Forms, Currents, Harmonic Forms,'', Translated from the French by F. R. Smith, 266 (1984).
|
[4] |
H. Federer, "Geometric Measure Theory,'', Die Grundlehren der mathematischen Wissenschaften, (1969).
|
[5] |
C. Hsiung, "A First Course in Differential Geometry,'', Pure and Applied Mathematics, (1981).
|
[6] |
D. Maharam, On the planar representation of a measurable subfield,, in, 1089 (1984), 47.
|
[7] |
V. Rohlin, On the fundamental ideas of measure theory,, Amer. Math. Soc. Translation, 1952 (1952).
|
[8] |
S. Srivastava, "A Course on Borel Sets,'', Graduate Texts in Mathematics, 180 (1998).
|
[9] |
S. Willard, "General Topology,'', Reprint of the 1970 original [Addison-Wesley, (1970).
|
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