Category:Definitions/Upper Darboux Integral

This category contains definitions related to Upper Darboux Integral.
Related results can be found in Category:Upper Darboux Integral.

Let $\closedint a b$ be a closed real interval.

Let $f: \closedint a b \to \R$ be a bounded real function.

The upper Darboux integral of $f$ over $\closedint a b$ is defined as:

$\ds \overline {\int_a^b} \map f x \rd x = \inf_P \map U P$

where:

the infimum is taken over all subdivisions $P$ of $\closedint a b$

$\map U P$ denotes the upper Darboux sum of $f$ on $\closedint a b$ belonging to $P$.