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[Merged by Bors] - refactor(measure_theory/l1_space): remove one of the two definitions of L1 space #6058
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src/measure_theory/l1_space.lean
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| Such a predicate is already available under the name `mem_ℒp 1`. We give a direct definition which | ||
| is easier to use, and show that it is equivalent to `mem_ℒp 1` | ||
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| In the second part, we establish an API between API and the space `L¹` of equivalence classes of |
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"API between API and ..." Is it intentional?
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LGTM |
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…of L1 space (#6058) Currently, we have two independent versions of the `L^1` space in mathlib: one coming from the general family of `L^p` spaces, the other one is an ad hoc construction based on the `integrable` predicate used in the construction of the Bochner integral. We remove the second construction, and use instead the `L^1` space coming from the family of `L^p` spaces to construct the Bochner integral. Still, we keep the `integrable` predicate as it is generally useful, and show that it coincides with the `mem_Lp 1` predicate.
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…of L1 space (#6058) Currently, we have two independent versions of the `L^1` space in mathlib: one coming from the general family of `L^p` spaces, the other one is an ad hoc construction based on the `integrable` predicate used in the construction of the Bochner integral. We remove the second construction, and use instead the `L^1` space coming from the family of `L^p` spaces to construct the Bochner integral. Still, we keep the `integrable` predicate as it is generally useful, and show that it coincides with the `mem_Lp 1` predicate.
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Currently, we have two independent versions of the
L^1space in mathlib: one coming from the general family ofL^pspaces, the other one is an ad hoc construction based on theintegrablepredicate used in the construction of the Bochner integral.We remove the second construction, and use instead the
L^1space coming from the family ofL^pspaces to construct the Bochner integral. Still, we keep theintegrablepredicate as it is generally useful, and show that it coincides with themem_Lp 1predicate.