Champernowne Constant is Normal

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Theorem

The Champernowne constant:

$0 \cdotp 12345 \, 67891 \, 01112 \, 13141 \, 51617 \, 18192 \, 02122 \ldots$

is normal.


Proof


Historical Note

The Champernowne constant was constructed by David Gawen Champernowne as an example of a real number which was demonstrably normal.

He did this in the paper of 1933: The Construction of Decimals Normal in the Scale of Ten (J. London Math. Soc. Vol. 8: 254 – 260), while still an undergraduate.


Sources