Recent content by mehr1methanol

Does geometric random variable work?

This is due tomorrow. Please help!

Example where X is not in the Lebesgue linear space. Homework Statement I'm trying to find an example where \lim_{n \to +\infty} P(|X|>n) = 0 but X \notin L where L is the Lebesgue linear space. Relevant equations: X is a random variabel, P is probability. I is indicator function. The...

I'm trying to find a counterexample where \lim_{n \to +\infty} P(|X|>n) = 0 but X \notin L where L is the lebesgue linear space. ∫|X|I(|X|>n)dp + ∫|X|I(|X|≤n)dp = ∫|X|dp therefore ∫nI(|X|>n)dp + ∫|X|I(|X|)dp ≤ ∫|X|dp Suppose ∫I(|X|>n)dp = 1/(n ln n) Clearly the hypothesis is satisfied...

That's exactly right. Thank you for pointing that out. I corrected the question. The reason for the repeats is the following: I'm preforming a symmetrization on the set K and the algorithm is such that it produces the above sequence. I got confused myself because once I got the...

Conjecture Regarding Rotation of a Set by a Sequence of Angles. Consider the following sequence, where the elements are rational numbers mulriplied by \pi: (\alpha_{i}) = \hspace{2 mm}\pi/4,\hspace{2 mm} 3\pi/8,\hspace{2 mm} \pi/4,\hspace{2 mm} 3\pi/16,\hspace{2 mm} \pi/4,\hspace{2 mm}...

I should admit your example is much more clever.

Yes for sure! I actually solved this problem a while ago! It turns out the conjecture doesn't hold and the counterexample is the van der corput sequence.

Def: A low discrepancy sequence is a uniformly distributed sequence with minimal discrepancy, O(logN/N). Question: Let <x> denote the fractal part of an irrational number x. Let (<x_n>) be an arbitrary low discrepancy sequence. Is it always true that : \lim_{n \to +\infty}|<x_n - x_{n-1}> -...