feat(MeasureTheory): add Resolvent (Stieltjes/Cauchy) Transform

[DavidLedvinka]

This PR adds the definition of the resolventTransform of a measure and some API. This is a non-standard notion that generalizes both the Stieltjes Transform and Cauchy Transform of a (real-valued) measure so that (for example) the proof that these transforms define holomorphic functions off the support of the measure can be given for both at once. Perhaps these important special cases could be made into abbrevs?

• depends on: feat(Analysis): add resolvent derivatives in the algebra component  #37172

[github-actions]

PR summary 772c92fec9

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.MeasureTheory.Measure.ResolventTransform (new file)	2626

---

Declarations diff

+ analyticOn_resolventTransform
+ hasDerivAt_resolvent'
+ hasDerivAt_resolventTransform
+ hasFDerivAt_resolvent
+ integrable_resolvent
+ measurable_resolvent
+ norm_resolvent_le_inv_infDist_support
+ resolventTransform
+ resolventTransform_apply
+ resolventTransform_def
+ resolventTransform_dirac
+ resolventTransform_zero_measure
+ resolvent_zero_of_mem_spectrum

You can run this locally as follows

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

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

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

---

No changes to technical debt.

You can run this locally as

./scripts/reporting/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).

[mathlib-dependent-issues]

This PR/issue depends on:

• feat(Analysis): add resolvent derivatives in the algebra component  #37172
  By Dependent Issues (🤖). Happy coding!