From: "Clive Tooth" <clive@pisquaredoversix.force9.co.uk>
Subject: Re: Pi
Date: Wed, 29 Mar 2000 13:39:37 +0100
Newsgroups: sci.math
Summary: [missing]

Simon Kristensen wrote...

>"Dan Goodman" <dog AT fcbob DOT demon DOT co DOT uk> writes:
>
>> > ... I also seem to recall, that almost every
>> > real is normal, but I'm not sure about this one.
>>
>> Can anyone comment about whether this is true or not? If it is, what does it
>> mean to say "almost every real is normal", does it mean that the set of
>> reals that aren't normal has measure 0? Thanks,
>
>The sense in which I seem to recall that almost every real is normal
>is indeed the sense that the set of non-normal numbers has Lebesgue
>measure 0.

Yes.


>As i recall the definition given of a normal number in this
>context, this was that every finite configuration of numbers occures
>in the decimal expansion.

Not quite. Gerry Myerson defined "normal" earlier in this thread.


>Unfortunately, the speaker at the seminar
>didn't give a reference on this point. I expect that if you pick up a
>recent book on number theory, you will find the result somewhere in
>there. Sorry to be of so little help.

"Almost all numbers are normal" is proved in Borel, E. (1909) Rend. Circ.
Mat. Palermo 27, 247-271


--
Clive Tooth
http://www.pisquaredoversix.force9.co.uk/
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