Timeline for Projective family of probability spaces
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Apr 11, 2015 at 18:19 | vote | accept | Exterior | ||
| Apr 5, 2015 at 0:08 | answer | added | kirk sturtz | timeline score: 3 | |
| Mar 31, 2015 at 19:15 | comment | added | Exterior | @LiviuNicolaescu I'm sure you are right. Andreas Blass's comment helped me understand that the measure is another piece of structures one should ask the arrows to respect. | |
| Mar 31, 2015 at 19:13 | comment | added | Liviu Nicolaescu | @Exterior I do not understand your comment. The arrows do matter. Think of the ring of $2$-adics $\mathbb{Z}_{(2)}$ vs. the ring of $3$-adics $\mathbb{Z}_{(3)}$. They're defined by identical diagrams, but the meaning of arrows is different. The result is nonisomorphic local rings. | |
| Mar 31, 2015 at 19:09 | comment | added | Andreas Blass | Liviu is right. In a category of probability spaces, one wants morphisms that respect the whole probability space structure, not just the $\sigma$-algebra but also the measure. | |
| Mar 31, 2015 at 18:59 | comment | added | Exterior | @LiviuNicolaescu that feels artificial though. Usually, compatibility conditions come from unraveling the definitions of limit, not from the arrows themselves. | |
| Mar 31, 2015 at 18:57 | comment | added | Liviu Nicolaescu | How about the category of probability spaces $(\Omega, \mathscr{O}, P)$ where morphisms are measurable maps $(\Omega_0,\mathscr{O}_0,P_0)\to (\Omega_1,\mathscr{O}_1,P_1)$ such that $f_*P_0=P_1$. | |
| Mar 31, 2015 at 18:40 | history | asked | Exterior | CC BY-SA 3.0 |