Energy–depth relationship in a rectangular channel

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In information theory, Shearer's inequality states that if X₁, ..., X_d are random variables and S₁, ..., S_n are subsets of {1, 2, ..., d} such that every integer between 1 and d lies in exactly r of these subsets, then

$H[(X_1,\dots ,X_d)]\le \frac{1}{r}\sum _{i=1}^{n}H[(X_j{)}_{j\in S_i}]$

where $(X_j{)}_{j\in S_i}$ is the Cartesian product of random variables $X_j$ with indices j in $S_i$ (so the dimension of this vector is equal to the size of $S_i$).