Commit 2021-02-10 00:03 49e50ee5
View on Github →feat(measure_theory/lp_space): add more API on Lp spaces (#6042)
Flesh out the file on L^p
spaces, notably adding facts on the composition with Lipschitz functions. This makes it possible to define in one go the positive part of an L^p
function, and its image under a continuous linear map.
The file ae_eq_fun.lean
is split into two, to solve a temporary issue: this file defines a global emetric space instance (of L^1
type) on the space of function classes. This passes to subtypes, and clashes with the topology on L^p
coming from the distance. This did not show up before as there were not enough topological statements on L^p
, but I have been bitten by this when adding new results. For now, we move this part of ae_eq_fun.lean
to another file which is not imported by lp_space.lean
, to avoid the clash. This will be solved in a subsequent PR in which I will remove the global instance, and construct the integral based on the specialization of L^p
to p = 1
instead of the ad hoc construction we have now (note that, currently, we have two different L^1
spaces in mathlib, denoted Lp E 1 μ
and α →₁[μ] E
-- I will remove the second one in a later PR).