TITLE: Proof of the transcendence of the Champernowne Constant with Thue-Siegel-Roth
QUESTION [6 upvotes]: It is well know that the Champernowne Constant 
0,1234567891011121314151617....
is transcendental. This was shown by Kurt Mahler in 1937. But the proof of the transcendence should also work with the famous Thue-Siegel-Roth theorem (http://en.wikipedia.org/wiki/Thue%E2%80%93Siegel%E2%80%93Roth_theorem), that was proved in 1955. 
I'm looking for a reference of the transcendence-proof where this theorem is used.

REPLY [9 votes]: Here is an extract from van der Poorten's "Obituary. Kurt Mahler (1903--1988)" (see p.353 in J. Austral. Math. Soc. Ser. A 51 (1991)):

In a more unexpected way, Mahler's
  arguments led to the following amusing
  result: Suppose $f$ is a non-constant
  polynomial taking integer values at
  the nonnegative integers. Then the
  concatenated decimal $$
> \phi=0.f(1)f(2)f(3)\dots $$ is
  transcendental. In particular
  Champernowne's normal number $$
> 0.123\dots910111213\dots $$ is transcendental. Mahler's argument
  relies on the observation that one
  readily obtains rational
  approximations to $\phi$ with
  denominators high powers of the base
  10, thus composed of the primes 2 and
  5 alone. Perhaps disappointingly,
  Roth's definitive form of the
  Thue--Siegel inequalities permits a
  more immediate argument obviating the
  need for an appeal to the $p$-adic
  results.

This is to say that Roth's argument is more superior than Mahler's but it appeared some 20 years later...