06A05-InfimumAndSupremumOfSumAndProduct.tex

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\pmtitle{infimum and supremum of sum and product}
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\begin{document}
Suppose that the real functions $f$ and $g$ are defined on an interval $\Delta$.\, Then on this interval
\begin{itemize}
\item $\inf(f\!+\!g) \;\geqq\; \inf f+\inf g$
\item $\sup(f\!+\!g) \;\leqq\; \sup f+\sup g$
\end{itemize}

If $f$ and $g$ are also nonnegative on $\Delta$, we can write
\begin{itemize}
\item $\inf(fg) \;\geqq\; \inf f\cdot\inf g$
\item $\sup(fg) \;\leqq\; \sup f\cdot\sup g$
\end{itemize}


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