Commit 2023-12-20 19:25 051aa734
View on Github →feat: non-integrability results of derivatives on [a, +oo)
(#8712)
We have in the library the lemma not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter
, saying that if a function tends to infinity at a point in an interval [a, b]
, then its derivative is not interval-integrable on [a, b]
. We generalize this result to allow for any set instead of [a, b]
, and apply it to half-infinite intervals.
In particular, we characterize integrability of x^s
on [a, +oo)
, and deduce that x^s
is never integrable on [0, +oo)
. This makes it possible to remove one assumption in Lemma mellin_comp_rpow
on the Mellin transform.