Consider the following map f:[0, 1] -> [0,1]. 10x, for 0 x < 1/10; f(x)=1,...

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Consider the following map f:[0, 1] -> [0,1]. 10x, for 0 ≤ x < 1/10; f(x)=1, for 1/10 < x < 9/10; 10 10x, for 9/10 ≤ x ≤ 1. Show that after a finite number of iterations, almost every point in [0,1] goes to Consider the following map f:[0, 1] -> [0,1]. 10x, for 0 ≤ x < 1/10; f(x)=1, for 1/10 < x < 9/10; 10 10x, for 9/10 ≤ x ≤ 1. Show that after a finite number of iterations, almost every point in [0,1] goes to