A Strong Hot Spot Theorem
نویسنده
چکیده
A real number α is said to be b-normal if every mlong string of digits appears in the base-b expansion of α with limiting frequency b−m. We prove that α is b-normal if and only if it possesses no base-b “hot spot.” In other words, α is b-normal if and only if there is no real number y such that smaller and smaller neighborhoods of y are visited by the successive shifts of the base-b expansion of α with larger and larger frequencies, relative to the lengths of these neighborhoods.
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