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Compactness of Invariant Densities for Families of Expanding, Piecewise Monotonic Transformations
Let I = [0,1] and let be the space of all integrable functions on I , where m denotes Lebesque measure on I . Let ∥ ∥ 1 be the ℒ- 1 -norm and let be a measurable, nonsingular transformation on I . Let denote the space of densities. The …