Arithmetic sequence in a Lebesgue measurable set Let $A\subseteq[a,b]$ be Lebesgue measurable, such that: $m(A)>\frac{2n-1}{2n}(b-a)$. I need to show that $A$ contains an arithmetic sequence with n numbers ($a_1,a_1+d,...,a_1+(n-1)*d$ for some d).
I thought about dividing [a,b] into n equal parts, and show that if I put one part on top of the other, there must be at least one lapping point, that will occur in every part. but I haven't succeeded in showing that.
Thank you.

Hint: You are on the right track. Have you noticed that the length of each of
your sub-intervals is $\frac{b-a}{n}$, while the total length of all the missing pieces is only $\frac{b-a}{2n}$?
