7

Part of 2017 Miklós Schweitzer

Problems(1)

Set covers <s_n fraction of interval

Source: Miklós Schweitzer 2017, problem 7

Characterize all increasing sequences

(s_n)

of positive reals for which there exists a set

I

with positive measure such that

\lambda(A\cap I)<\frac{s_n}{n}

holds for every interval

I

1/n

\lambda

denotes the Lebesgue measure.

measureMeasure theoryintervalreal analysiscollege contestsMiklos Schweitzer