Timeline for Measure induced on [0, 1] by infinite tosses of biased coin
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 23, 2016 at 17:32 | comment | added | Yuval Peres | This classical argument can give more, namely the Hausdorff dimension of the measures $\mu_p$ and the sets $A_p$. For an exposition and references see, e.g., math.stonybrook.edu/~bishop/Bishop_Peres_Jan_22_2015.pdf | |
| Sep 20, 2016 at 23:59 | comment | added | Nate Eldredge | @Anindya: Sort of, but proving the strong law in this case isn't particularly difficult. | |
| Sep 20, 2016 at 23:23 | comment | added | Anindya | This is a truly excellent answer. I am keeping this as Exhibit A for how a probabilistic argument neatly proves a result which seems very intractable by analysis type techniques. I suspect the "hard analysis" part goes into proving the strong law of large numbers. | |
| Sep 20, 2016 at 23:20 | vote | accept | Anindya | ||
| Sep 20, 2016 at 17:28 | comment | added | Gerald Edgar | When you have a hammer, everything looks like a nail. I agree that a more elementary argument (such as Nate's) is better. | |
| Sep 20, 2016 at 8:50 | comment | added | Anthony Quas | This is a nice answer - I think it's essentially the same as mine, but yours has the advantage of relying on more well-known technology (the SLLN). | |
| Sep 20, 2016 at 3:31 | history | answered | Nate Eldredge | CC BY-SA 3.0 |