# 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).