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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 762031430, 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). Google Scholar 
[2] 
D. Cohn, "Measure Theory,'', Reprint of the 1980 original, (1980). Google Scholar 
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G. de Rham, "Differentiable Manifolds. Forms, Currents, Harmonic Forms,'', Translated from the French by F. R. Smith, 266 (1984). Google Scholar 
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H. Federer, "Geometric Measure Theory,'', Die Grundlehren der mathematischen Wissenschaften, (1969). Google Scholar 
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C. Hsiung, "A First Course in Differential Geometry,'', Pure and Applied Mathematics, (1981). Google Scholar 
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D. Maharam, On the planar representation of a measurable subfield,, in, 1089 (1984), 47. Google Scholar 
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V. Rohlin, On the fundamental ideas of measure theory,, Amer. Math. Soc. Translation, 1952 (1952). Google Scholar 
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S. Srivastava, "A Course on Borel Sets,'', Graduate Texts in Mathematics, 180 (1998). Google Scholar 
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S. Willard, "General Topology,'', Reprint of the 1970 original [AddisonWesley, (1970). Google Scholar 
show all references
References:
[1] 
H. Bergström, "Weak Convergence of Measures,'', Probability and Mathematical Statistics, (1982). Google Scholar 
[2] 
D. Cohn, "Measure Theory,'', Reprint of the 1980 original, (1980). Google Scholar 
[3] 
G. de Rham, "Differentiable Manifolds. Forms, Currents, Harmonic Forms,'', Translated from the French by F. R. Smith, 266 (1984). Google Scholar 
[4] 
H. Federer, "Geometric Measure Theory,'', Die Grundlehren der mathematischen Wissenschaften, (1969). Google Scholar 
[5] 
C. Hsiung, "A First Course in Differential Geometry,'', Pure and Applied Mathematics, (1981). Google Scholar 
[6] 
D. Maharam, On the planar representation of a measurable subfield,, in, 1089 (1984), 47. Google Scholar 
[7] 
V. Rohlin, On the fundamental ideas of measure theory,, Amer. Math. Soc. Translation, 1952 (1952). Google Scholar 
[8] 
S. Srivastava, "A Course on Borel Sets,'', Graduate Texts in Mathematics, 180 (1998). Google Scholar 
[9] 
S. Willard, "General Topology,'', Reprint of the 1970 original [AddisonWesley, (1970). Google Scholar 
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