Timeline for Uniform inverse-measure-preserving function for some class of measures
Current License: CC BY-SA 3.0
4 events
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| Jun 14, 2011 at 12:18 | history | edited | Gerald Edgar | CC BY-SA 3.0 |
added 365 characters in body
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| Jun 13, 2011 at 19:20 | comment | added | Archimondain | ps : What I call bernoulli measures are measures on $2^\omega$ such that $\mu(0)+\mu(1)=1$ and for any basic open $x_1 \dots x_n$, we have $\mu(x_1 \dots x_n))=\mu(x_1) \times \dots \times \mu(x_n)$ where each $x_i$ is either $0$ or $1$. | |
| Jun 13, 2011 at 19:19 | comment | added | Archimondain | Thank you very much for your answer, and sorry for the lack of precision. Yes I mean the natural Borel sigma-algebra, and yes I mean probability measures. The thing is that I would like to have the same function $f$ for several measures. As an example, I think the class of Bernoulli measures have that. If you take the function which spit a string in blocks of two bits and transform $01$ to $0$, $10$ to $1$ and $00$ and $11$ to the empty string, then I am pretty sure that lebesgue measure is the image of $\nu$ with the same function $f$ for any bernoulli measure $\nu$ | |
| Jun 13, 2011 at 16:50 | history | answered | Gerald Edgar | CC BY-SA 3.0 |