Notes of the seminar Evolution Equations in Probability Spaces and the Continuity Equation
نویسنده
چکیده
1 Probability measures on metric spaces 1 1.1 Borel sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Borel probability measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Narrow convergence of measures . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 The bounded Lipschitz metric . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Measures as functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.6 Prokhorov’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.7 Disintegration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.8 Borel probability measures with respect to weak topologies . . . . . . . . . 20 1.9 Transport of measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
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