infimum and supremum of sum and product

Suppose that the real functions f and g are defined on an interval Δ.  Then on this interval

  • inf(f+g)inff+infg

  • sup(f+g)supf+supg

If f and g are also nonnegative on Δ, we can write

  • inf(fg)inffinfg

  • sup(fg)supfsupg

Title infimum and supremum of sum and product
Canonical name InfimumAndSupremumOfSumAndProduct
Date of creation 2013-03-22 19:01:25
Last modified on 2013-03-22 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