What fails in a “lower-sum-only” extension of Riemann integration? – math.stackexchange.com
Celestina
In Riemann integration, one defines both lower and upper sums $
L(f,P), U(f,P),
$
and declares a bounded function $f:[a,b]\to\mathbb{R} $ to be integrable if
$
\sup_P L(f,P)=\inf_P U(f,P).
$
On the ...