Matematiikassa Milnen epäyhtälö on positiivisia reaalilukuja koskeva epäyhtälö [ 1]
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{\displaystyle \left(\sum _{i=1}^{n}(a_{i}+b_{i})\right)\left(\sum _{i=1}^{n}{\frac {a_{i}b_{i}}{a_{i}+b_{i}}}\right)\leq \left(\sum _{i=1}^{n}a_{i}\right)\left(\sum _{i=1}^{n}b_{i}\right)}
yleistetyn Milnen epäyhtälön [ 2]
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{\displaystyle \left(\sum _{i=1}^{n}(a_{i}+b_{i}+c_{i})\right)\left(\sum _{i=1}^{n}{\frac {a_{i}b_{i}+b_{i}c_{i}+a_{i}c_{i}}{a_{i}+b_{i}+c_{i}}}\right)\left(\sum _{i=1}^{n}{\frac {a_{i}b_{i}c_{i}}{a_{i}b_{i}+b_{i}c_{i}+a_{i}c_{i}}}\right)\leq \left(\sum _{i=1}^{n}a_{i}\right)\left(\sum _{i=1}^{n}b_{i}\right)\left(\sum _{i=1}^{n}c_{i}\right)}
