A strongly normal number to base 
is a real number that is simply strongly normal to base 
for every positive integer 
(Belshaw and Borwein 2013). Every strongly
normal number is a normal number. Belshaw and Borwein
(2013) introduced strong normality and proved that the binary
Champernowne constant is not strongly normal in base 2.
Strongly Normal Number
See also
Binary Champernowne Constant, Law of the Iterated Logarithm, Normal NumberExplore with Wolfram|Alpha
References
Belshaw, A. and Borwein, P. "Champernowne's Number, Strong Normality, and the X Chromosome." In Computational and Analytical Mathematics: In Honor of Jonathan Borwein's 60th Birthday (Ed. D. H. Bailey, H. H. Bauschke, P. Borwein, F. Garvan, M. Théra, J. D. Vanderwerff, and H. Wolkowicz). New York: Springer, pp. 29-44, 2013. https://doi.org/10.1007/978-1-4614-7621-4_3.Cite this as:
Weisstein, Eric W. "Strongly Normal Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StronglyNormalNumber.html