### Normal numbers and self-similar measures.

Ergodic Theory and Dynamical Systems Seminar

14th October 2021, 2:00 pm – 3:00 pm

Fry Building, 2.04

A real number x is said to be normal in base b if the sequence (b^{n} x) is uniformly distributed modulo one. In this talk I will discuss a recent result which states that for a self-similar measure and an integer b, if the self-similar measure and b satisfy a weak arithmetic assumption, then almost every x is normal in base b with respect to the self-similar measure.

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