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SUMMARY:Meng Wu (Oulun yliopisto)
DTSTART:20250401T120000Z
DTEND:20250401T130000Z
DTSTAMP:20260423T021439Z
UID:OWNS/146
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/146/">O
 n normal numbers in fractals</a>\nby Meng Wu (Oulun yliopisto) as part of 
 One World Numeration seminar\n\n\nAbstract\nLet $K$ be the ternary Cantor 
 set\, and let $\\mu$ be the Cantor–Lebesgue measure on $K$. It is well k
 nown that every point in $K$ is not 3-normal. However\, if we take any nat
 ural number $p \\ge 2$ that is not a power of 3\, then $\\mu$-almost every
  point in $K$ is $p$-normal. This classical result is due to Cassels and W
 . Schmidt.\n\nAnother way to obtain normal numbers from K is by rescaling 
 and translating $K$\, then examining the transformed set. A recent nice re
 sult by Dayan\, Ganguly\, and Barak Weiss shows that for any irrational nu
 mber $t$\, for $\\mu$-almost all $x \\in K$\, the product $tx$ is 3-normal
 .\n\nIn this talk\, we will discuss these results and their generalization
 s\, including replacing $p$ with an arbitrary beta number and considering 
 more general times-3 invariant measures instead of the Cantor–Lebesgue m
 easure.\n
LOCATION:https://researchseminars.org/talk/OWNS/146/
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