Category:Lower Darboux Integral

This category contains results about Lower Darboux Integral.
Definitions specific to this category can be found in Definitions/Lower Darboux Integral.

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

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

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

$\ds \underline {\int_a^b} \map f x \rd x = \sup_P \map L P$

where:

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

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