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Apr 15, 2012 at 9:52 comment added user20886 For some reason i can't edit, but the range in question is $[0,1)$ and the digital representation is all those digits occurring after the decimal point.
Apr 15, 2012 at 9:51 comment added user20886 I might add that you can instead define the probability space to be the reals $[\0 \ldots 1)$. Then for a particular real you take it's digital representation in base $k$ as your sequence. This is essentially the same as your answer, except you get the structure of the sigma-algebra and probability space "for free".
Apr 15, 2012 at 9:06 vote accept user20886
Apr 9, 2012 at 11:19 history edited Did CC BY-SA 3.0
deleted 34 characters in body; added 10 characters in body; deleted 1 characters in body
Apr 9, 2012 at 11:13 history answered Did CC BY-SA 3.0