MathDB

Inequality on intervals

Source: Miklós Schweitzer 2014, P2

December 22, 2014

inequalitiesfunctionintegrationcombinatorics proposedcombinatorics

Problem Statement

Let

k\geq 1

and let

I_{1},\dots, I_{k}

be non-degenerate subintervals of the interval

[0, 1]

. Prove that

\sum \frac{1}{\left | I_{i}\cup I_{j} \right |} \geq k^{2}

where the summation is over all pairs

(i, j)

of indices such that

I_i\cap I_j\neq \emptyset