feat(MeasureTheory/Integral/Bochner/Set): add setIntegral_union'

[lakesare]

From the Carleson project.

---

Upstreaming from Carleson: /Carleson/ToMathlib/MeasureTheory/Integral/Bochner/ContinuousLinearMap.lean

In this PR

theorem setIntegral_union'

Renamed: from MeasureTheory.setIntegral_union_2 to MeasureTheory.setIntegral_union'.
Signature: changed from [MeasurableSpace X] to {mX : MeasurableSpace X} (to match existing section variables).

-- CARLESON
MeasureTheory.setIntegral_union_2.{u_1, u_2} {X : Type u_1} {E : Type u_2} [NormedAddCommGroup E]
[NormedSpace ℝ E] {f : X → E} {s t : Set X} {μ : Measure X} (hst : Disjoint s t)
(ht : MeasurableSet t) (ht : MeasurableSet t) (hfst : IntegrableOn f (s ∪ t) μ)
[MeasurableSpace X]
: ∫ (x : X) in s ∪ t, f x ∂μ = ∫ (x : X) in s, f x ∂μ + ∫ (x : X) in t, f x ∂μ
-- MATHLIB
MeasureTheory.setIntegral_union'.{u_1, u_3} {X : Type u_1} {E : Type u_3} [NormedAddCommGroup E]
[NormedSpace ℝ E] {f : X → E} {s t : Set X} {μ : Measure X} (hst : Disjoint s t)
(ht : MeasurableSet t) (ht : MeasurableSet t) (hfst : IntegrableOn f (s ∪ t) μ)
{mX : MeasurableSpace X}
: ∫ (x : X) in s ∪ t, f x ∂μ = ∫ (x : X) in s, f x ∂μ + ∫ (x : X) in t, f x ∂μ

[github-actions]

PR summary 0be4893e96

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ setIntegral_union'

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.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 0be4893).

• +1 new declarations
• −0 removed declarations

+MeasureTheory.setIntegral_union'

---

No changes to strong technical debt.
No changes to weak technical debt.

Current commit 0be4893e96
Reference commit 7954be2d94

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.py 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).

[lakesare]

carleson

[lakesare]

easy