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| | #REDIRECT [[Shearer's inequality]] |
| | |
| | If <math>X_{1},...X_{d}</math> are random variables and <math>S_{1},...,S_{n}</math> are subsets of <math>\{1,2,...,d\}</math> such that every integer between ''1'' and ''d'' lie in exactly ''r'' of these subsets, then |
| | :<math> H[(X_{1},...,X_{d})]\leq \frac{1}{r}\sum_{i=1}^{n}H[(X_{j})_{j\in S_{i}}]</math> |
| | where <math> (X_{j})_{j\in S_{i}}</math> is the Cartesian product of random variables <math>X_{j}</math> with indexes ''j'' in <math>S_{i}</math> (so the dimension of this vector is equal to the size of <math>S_{i}</math>). |
Revision as of 09:53, 11 June 2013
If are random variables and are subsets of such that every integer between 1 and d lie in exactly r of these subsets, then
where is the Cartesian product of random variables with indexes j in (so the dimension of this vector is equal to the size of ).