[FOM] Concerning Probability Measures
Robert M. Solovay
solovay at Math.Berkeley.EDU
Sat Feb 18 19:39:49 EST 2006
I just want to add a small addition to my previous reply.
On Sat, 18 Feb 2006, Robert M. Solovay wrote:
>
>> I am sure that you noticed that it is a translation invariant extension of
>> Lebesgue measure in these models. Furthermore, I would assume that any
>> Lebesgue measure preserving automorphism of R remains measure preserving?
>
> Yes to both your questions.
Addendum: I am assuming that the automorphism which preserves Lebesgue
measure is a Borel map. Perhaps this is not needed. It holds in all the
obvious examples. {Say when R is replaced by the homogeneous space of a
Lie group G [carrying an invariant measure] and one wants to see that the
action of G preserves the extension mu.}
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