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Inequality for reals in [0,1]

Source: Mediterranean MO 2006

October 30, 2010
inequalitiesinequalities proposed

Problem Statement

Let 0≤xi,j≤10\le x_{i,j} \le 1, where i=1,2,…mi=1,2, \ldots m and j=1,2,…nj=1,2, \ldots n. Prove the inequality
∏j=1n(1−∏i=1mxi,j)+∏i=1m(1−∏j=1n(1−xi,j))≥1 \prod_{j=1}^n\left(1-\prod_{i=1}^mx_{i,j} \right)+ \prod_{i=1}^m\left(1-\prod_{j=1}^n(1-x_{i,j}) \right) \ge 1
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