infimum and supremum of sum and product
Suppose that the real functions $f$ and $g$ are defined on an interval $\mathrm{\Delta}$. Then on this interval

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$inf(f+g)\geqq inff+infg$

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$sup(f+g)\leqq supf+supg$
If $f$ and $g$ are also nonnegative on $\mathrm{\Delta}$, we can write

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$inf(fg)\geqq inff\cdot infg$

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$sup(fg)\leqq supf\cdot supg$
Title  infimum and supremum of sum and product 

Canonical name  InfimumAndSupremumOfSumAndProduct 
Date of creation  20130322 19:01:25 
Last modified on  20130322 19:01:25 
Owner  pahio (2872) 
Last modified by  pahio (2872) 
Numerical id  4 
Author  pahio (2872) 
Entry type  Theorem 
Classification  msc 06A05 
Classification  msc 26D15 
Related topic  ProductAndQuotientOfFunctionsSum 