Commit 2023-05-25 17:14 6480bedf
View on Github →chore(measure_theory/function/lp_space): add nnnorm lemmas (#19091)
This also adds a has_nnnorm (Lp E p μ)
instance, which applies more generally (without [fact (1 ≤ p)]
) than the version derived from Lp.normed_add_comm_group
.
In general, nnnorm
(‖f x‖₊)
statements can often be easier to work with because there is no need to repeatedly remind Lean that the norm is non-negative. Most of the time, the norm
(‖x‖
) counterparts follow trivially from the nnnorm
ones.
Notably this removes the need for a proof-by-cases in snorm_le_mul_snorm_of_ae_le_mul
and some similar lemmas.