feat(Topology/MetricSpace): the L^1 direct sum of metric spaces#40212
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YaelDillies wants to merge 3 commits into
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feat(Topology/MetricSpace): the L^1 direct sum of metric spaces#40212YaelDillies wants to merge 3 commits into
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Also fix the variable implicitness and and names of a few existing declarations. Renames: * `coe_finsetSum` to `ofNNReal_finsetSum` * `coe_finsetProd` to `ofNNReal_finsetProd`
PR summary ceebb372a9
|
| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.Data.NNReal.Basic | 927 | 940 | +13 (+1.40%) |
| Mathlib.Data.ENNReal.BigOperators | 936 | 949 | +13 (+1.39%) |
| Mathlib.Topology.Algebra.InfiniteSum.ENNReal | 1317 | 1323 | +6 (+0.46%) |
Import changes for all files
| Files | Import difference |
|---|---|
75 filesMathlib.Algebra.Order.Archimedean.Real.Hom Mathlib.Algebra.Order.Star.Real Mathlib.Algebra.Star.CHSH Mathlib.Analysis.Asymptotics.Defs Mathlib.Analysis.BoxIntegral.Box.Basic Mathlib.Analysis.BoxIntegral.Partition.Basic Mathlib.Analysis.BoxIntegral.Partition.Split Mathlib.Analysis.BoxIntegral.Partition.Tagged Mathlib.Analysis.Calculus.TangentCone.Basic Mathlib.Analysis.Calculus.TangentCone.Defs Mathlib.Analysis.Calculus.TangentCone.Prod Mathlib.Analysis.Complex.Exponential Mathlib.Analysis.Complex.Norm Mathlib.Analysis.Complex.Order Mathlib.Analysis.Complex.Trigonometric Mathlib.Analysis.Normed.Field.Basic Mathlib.Analysis.Normed.Field.TransferInstance Mathlib.Analysis.Normed.Group.AddTorsor Mathlib.Analysis.Normed.Group.Basic Mathlib.Analysis.Normed.Group.Bounded Mathlib.Analysis.Normed.Group.CocompactMap Mathlib.Analysis.Normed.Group.Constructions Mathlib.Analysis.Normed.Group.Continuity Mathlib.Analysis.Normed.Group.Indicator Mathlib.Analysis.Normed.Group.Int Mathlib.Analysis.Normed.Group.Rat Mathlib.Analysis.Normed.Group.Real Mathlib.Analysis.Normed.Group.Subgroup Mathlib.Analysis.Normed.Group.Submodule Mathlib.Analysis.Normed.Module.ENormedSpace Mathlib.Analysis.Normed.Module.MStructure Mathlib.Analysis.Normed.Order.Basic Mathlib.Analysis.Normed.Order.Hom.Basic Mathlib.Analysis.Normed.Order.Hom.Ultra Mathlib.Analysis.Normed.Ring.Basic Mathlib.Analysis.Normed.Ring.Finite Mathlib.Analysis.Normed.Ring.TransferInstance Mathlib.Analysis.Normed.Ring.WithAbs Mathlib.Analysis.NormedSpace.Alternating.Basic Mathlib.Analysis.NormedSpace.Alternating.Curry Mathlib.Analysis.NormedSpace.Alternating.Uncurry.Fin Mathlib.Analysis.NormedSpace.Connected Mathlib.Analysis.NormedSpace.ENormedSpace Mathlib.Analysis.NormedSpace.Extr Mathlib.Analysis.NormedSpace.MStructure Mathlib.Analysis.NormedSpace.Multilinear.Basic Mathlib.Analysis.NormedSpace.Multilinear.Curry Mathlib.Analysis.NormedSpace.Normalize Mathlib.Analysis.NormedSpace.PiTensorProduct.InjectiveSeminorm Mathlib.Analysis.NormedSpace.PiTensorProduct.ProjectiveSeminorm Mathlib.Analysis.NormedSpace.RieszLemma Mathlib.Analysis.Rat.NatSqrt.Real Mathlib.Analysis.Real.Sqrt Mathlib.Analysis.SpecialFunctions.Log.ERealExp Mathlib.Analysis.SumOverResidueClass Mathlib.Data.Real.CompleteField Mathlib.InformationTheory.Hamming Mathlib.MeasureTheory.OuterMeasure.AE Mathlib.MeasureTheory.OuterMeasure.Basic Mathlib.MeasureTheory.OuterMeasure.BorelCantelli Mathlib.MeasureTheory.OuterMeasure.Operations Mathlib.Tactic.NormNum.RealSqrt Mathlib.Topology.Algebra.InfiniteSum.ENNReal Mathlib.Topology.Algebra.InfiniteSum.Field Mathlib.Topology.Algebra.InfiniteSum.Real Mathlib.Topology.Compactness.HilbertCubeEmbedding Mathlib.Topology.EMetricSpace.BoundedVariation Mathlib.Topology.Instances.ENNReal.ENatENNReal Mathlib.Topology.Instances.ENNReal.Lemmas Mathlib.Topology.Instances.EReal.Lemmas Mathlib.Topology.Instances.NNReal.Lemmas Mathlib.Topology.MetricSpace.CauSeqFilter Mathlib.Topology.Metrizable.CompletelyMetrizable Mathlib.Topology.Semicontinuity.Basic Mathlib.Topology.Semicontinuity.Lindelof |
6 |
4 filesMathlib.Algebra.Order.Floor.Extended Mathlib.Data.ENNReal.BigOperators Mathlib.Data.NNReal.Basic Mathlib.Topology.Metrizable.Uniformity |
13 |
Mathlib.Topology.MetricSpace.Finsupp (new file) |
1116 |
Declarations diff
+ dist_def
+ edist_def
+ instance [EMetricSpace X] : EMetricSpace (ι →₀ X)
+ instance [MetricSpace X] : MetricSpace (ι →₀ X)
+ instance [PseudoEMetricSpace X] : PseudoEMetricSpace (ι →₀ X)
+ instance [PseudoMetricSpace X] : PseudoMetricSpace (ι →₀ X)
+ nndist_def
+ ofNNReal_finsetProd
+ ofNNReal_finsetSum
+ ofNNReal_finsuppProd
+ ofNNReal_finsuppSum
+ toReal_finsuppProd
+ toReal_finsuppSum
You can run this locally as follows
## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>
## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.
No changes to strong technical debt.
No changes to weak technical debt.
Current commit ceebb372a9
Reference commit e577c1669e
This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary
- The
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
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| /-- The L^1 extended metric on `ι`-many copies of a metric space `X` -/ | ||
| noncomputable instance [PseudoEMetricSpace X] : PseudoEMetricSpace (ι →₀ X) where |
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I think we should make this be the L^∞ metric instead since that's what we do for the pi type.
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I thought about this and I in fact I believe L^1 is the right choice: The dual of a direct sum is a pi type, and therefore it makes sense for the dual norm of a direct sum to be the L^infty norm that we put on the pi type. The dual norm of the L^1 is the L^infty, which is why I think the direct sum should be equipped with the L^1 norm.
What do you think?
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Interesting angle.
I think it is more likely that people will be in a situation where ι is finite and want an isometry than they are to be in a situation where the duality matters. This might be worth raising on Zulip though.
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Endow the direct sum
ι →₀ Xofι-many copies of a metric spaceXwith the L^1 metric.It would be similarly easy to use the L^infty metric instead, but L^1 feels more appropriate as the default for the direct sum.