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Results tagged with measure-theory
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user 81488
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
13
votes
Measure induced on [0, 1] by infinite tosses of biased coin
Just a side comment: if you pass from binary to trinary, you can still obtain the Lebesgue measure by choosing the digits $0$, $1$, $2$, with probabilities $(\frac{1}{3},\frac{1}{3},\frac{1}{3})$ (som …
- 8,842
4
votes
Counterexample: weak convergence doesn't imply $L^1-$convergence
If, for $n>2$, $\mu_n$ puts masses $n^{-1},n^{-1}, 1-2n^{-1}$ at $2n, -n, -\frac{n}{n-2}$ respectively (so that $\mu$ puts the unit mass at $-1$), doesn't it work?
- 128k