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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:
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References:
[1] |
Engel John C Dela Vega, Robert J Elliott. Conditional coherent risk measures and regime-switching conic pricing. Probability, Uncertainty and Quantitative Risk, 2021, 6 (4) : 267-300. doi: 10.3934/puqr.2021014 |
[2] |
R.D.S. Oliveira, F. Tari. On pairs of differential $1$-forms in the plane. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 519-536. doi: 10.3934/dcds.2000.6.519 |
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Naoufel Ben Abdallah, Irene M. Gamba, Giuseppe Toscani. On the minimization problem of sub-linear convex functionals. Kinetic and Related Models, 2011, 4 (4) : 857-871. doi: 10.3934/krm.2011.4.857 |
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Angelo B. Mingarelli. Nonlinear functionals in oscillation theory of matrix differential systems. Communications on Pure and Applied Analysis, 2004, 3 (1) : 75-84. doi: 10.3934/cpaa.2004.3.75 |
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Shrikrishna G. Dani. Simultaneous diophantine approximation with quadratic and linear forms. Journal of Modern Dynamics, 2008, 2 (1) : 129-138. doi: 10.3934/jmd.2008.2.129 |
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[9] |
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Holger Heumann, Ralf Hiptmair. Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Discrete and Continuous Dynamical Systems, 2011, 29 (4) : 1471-1495. doi: 10.3934/dcds.2011.29.1471 |
[12] |
Dorina Mitrea and Marius Mitrea. Boundary integral methods for harmonic differential forms in Lipschitz domains. Electronic Research Announcements, 1996, 2: 92-97. |
[13] |
Dorina Mitrea, Irina Mitrea, Marius Mitrea, Lixin Yan. Coercive energy estimates for differential forms in semi-convex domains. Communications on Pure and Applied Analysis, 2010, 9 (4) : 987-1010. doi: 10.3934/cpaa.2010.9.987 |
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Huyên Pham. Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications. Probability, Uncertainty and Quantitative Risk, 2016, 1 (0) : 7-. doi: 10.1186/s41546-016-0008-x |
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[18] |
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[19] |
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[20] |
Teresa Faria. Normal forms for semilinear functional differential equations in Banach spaces and applications. Part II. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 155-176. doi: 10.3934/dcds.2001.7.155 |
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