Timeline for Tightness on a set $A$ implies tightness on a set $B$ where $A\subset B$?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14, 2021 at 8:57 | vote | accept | Mark | ||
| Jan 13, 2021 at 20:22 | comment | added | Mark | Thank you for the follow up. This helps me a lot. | |
| Jan 13, 2021 at 20:21 | comment | added | Iosif Pinelis | @Mark : Yes, as long as you the continuity, the tightness is preserved. | |
| Jan 13, 2021 at 19:51 | comment | added | Mark | Thank you for the answer. Your explanation is pretty good. This real makes my job easier because I don't need to show tightness again. I have showed tightness for a family of probability laws of the solutions of some system of spde in the space $A=C([0,T];H^r(\mathbb{R}))$. It is good to know that I don't need to do that again for the space $B=L^2(0,T;L^2(\mathbb{R}))$. Also if I am not mistaken space $B$ could also be for example $B=L^{\infty}(0,T;L^2(\mathbb{R}))$ or $B=L^2(0,T;L^{\infty}(\mathbb{R}))$ and similar because the emedding stays continuous? | |
| Jan 13, 2021 at 15:19 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |