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Let I = (0, 1] be the unit interval of the real line. For a given number a \in (0, 1) we define a map T : I \to I by the formula
if
{{ INVALID LATEX }}

Show that for every interval J \subset I there exists an integer n > 0 such that T^n(J) \cap  J \neq \emptyset.

Slični zadaci

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