Timeline for Rational valued functions on the Cantor set with $\int_{C} f^{3}d\mu=1 $
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 10, 2016 at 7:47 | vote | accept | Ali Taghavi | ||
| Feb 6, 2016 at 16:07 | comment | added | Anthony Quas | So here is a concrete example. Take $f$ to be $2^{-n}$ on $S_n$ for $n>0$ and $f=4/3$ on $S_0$. With a little more imagination, you could build $f$ that is $2^{-n}$ on each $S_n$ with $n>1$ simultaneously satisfying your 2 conditions. My argument shows that there are lots of these functions - the construction is very flexible. | |
| Feb 6, 2016 at 11:28 | comment | added | Ali Taghavi | @AnthonyQuas thank you for your answer. what is f precisely? | |
| Feb 4, 2016 at 21:45 | comment | added | Anthony Quas | Clearly the exact same argument will produce a function that is locally constant around no point if instead of defining $f$ to be constant on the cylinder sets, one defines $f$ to be a locally constant multiple of $1+\sum_{n=1}^\infty x_n 2^{-n}$. | |
| Feb 4, 2016 at 20:44 | comment | added | Gro-Tsen | The natural question follows: can we do a function which is locally constant around no point? | |
| Feb 4, 2016 at 20:27 | history | answered | Anthony Quas | CC BY-SA 3.0 |