[FOM] Concerning Probability Measures

[Robert M. Solovay]

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.}