Let 
be an infinite word over a finite alphabet 
. Then there exists a uniformly recurrent infinite word
such that 
,
where 
is the set of all finite subwords of 
.
Furstenberg's Theorem
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References
Allouche, J.-P. and Shallit, J. Automatic Sequences: Theory, Applications, Generalizations. Cambridge, England: Cambridge University Press, p. 337, 2003.Referenced on Wolfram|Alpha
Furstenberg's TheoremCite this as:
Weisstein, Eric W. "Furstenberg's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FurstenbergsTheorem.html