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Part of 2014 Miklós Schweitzer

Problems(1)

Inequality on intervals

Source: Miklós Schweitzer 2014, P2

12/22/2014
Let k≥1 k\geq 1 and let I1,…,Ik I_{1},\dots, I_{k} be non-degenerate subintervals of the interval [0,1] [0, 1] . Prove that ∑1∣Ii∪Ij∣≥k2 \sum \frac{1}{\left | I_{i}\cup I_{j} \right |} \geq k^{2} where the summation is over all pairs (i,j) (i, j) of indices such that Ii∩Ij≠∅I_i\cap I_j\neq \emptyset.
inequalitiesfunctionintegrationcombinatorics proposedcombinatorics