feat: haar measures on short exact sequences

[tb65536]

This PR defines the notion of a short exact sequence of topological groups, and proves that if 1 → A → B → C → 1 is a short exact sequence of topological groups, then Haar measures on A and C induce a Haar measure on B.

The final result of the file is a consequence needed for FLT: If B → C is injective on an open set U, then U has bounded measure.

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[github-actions[bot]]

PR summary 433c17180b

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Topology.Algebra.Group.Extension (new file)	812
Mathlib.MeasureTheory.Measure.Haar.Extension (new file)	1990

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Declarations diff

+ TopologicalAddGroup.IsSES + TopologicalGroup.IsSES + apply_apply + inducedMeasure + inducedMeasure_lt_of_injOn + inducedMeasure_regular + integral_inducedMeasure + integral_pullback_invFun_apply + integrate + integrate_apply + integrate_mono + isHaarMeasure_inducedMeasure + ofClosedSubgroup + pullback + pullback_def + pushforward + pushforward_apply + pushforward_def + pushforward_mono

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[RemyDegenne]

Could you add a PR description? It should describe what you are adding, and also help the reviewer understand why you are adding this (what do you want to do with it?).

[tb65536]

Could you add a PR description? It should describe what you are adding, and also help the reviewer understand why you are adding this (what do you want to do with it?).

Oops, sorry for overlooking this. Just added.