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Results tagged with limsup-and-liminf
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user 173490
For questions concerning limit superior and limit inferior of sequences (of real numbers and various generalizations) and also for $\limsup$ and $\liminf$ of sequences of sets.
4
votes
Accepted
Mean Cauchy sequences
The answer is yes. This solution was provided to us by Reddit user Ravinex.
The trick here is that we need to treat $N$ and $M$ independent. It turns out that it's not true if we only have $N=M$ in th …
- 6,155
4
votes
Accepted
Pathwise linearization of diffusion processes
This is true. We need the following result, essentially proven in this post.
Proposition: (Linearization of diffusion process)
With $X$ as in the problem statement, we have
$$ \mathbb E \left [\frac{\ …
- 6,155
1
vote
Is the $L^\infty$ norm of the derivative the same under the Hausdorff and Lebesgue measure?
Though far from a complete answer, the following answers the problem affirmatively for the case of integer $\frac{n}{2} \leq k < n$. It is based on the analogous result for the case $(0, n)$, proven h …
- 6,155