[Merged by Bors] - feat: generalize Hölder's inequality for sums to Real.HolderTriple

[j-loreaux]

Currently the API exists only for Real.HolderConjugate. This generalizes it in anticipation of #35197, which implements the Hölder framework for lp spaces.

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[github-actions]

PR summary d86a5de2ff

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ Lr_le_Lp_mul_Lq
+ Lr_le_Lp_mul_Lq_tsum
+ Lr_le_Lp_mul_Lq_tsum_of_nonneg
+ Lr_rpow_le_Lp_mul_Lq_of_nonneg
+ Lr_rpow_le_Lp_mul_Lq_tsum
+ Lr_rpow_le_Lp_mul_Lq_tsum_of_nonneg
+ inner_le_Lp_mul_Lq_of_nonneg'
+ summable_Lr_of_Lp_Lq_of_nonneg
+ summable_and_Lr_rpow_le_Lp_mul_Lq_tsum
+ summable_and_Lr_rpow_le_Lp_mul_Lq_tsum_of_nonneg
+ summable_and_inner_le_Lp_mul_Lq_tsum
+ summable_and_inner_le_Lp_mul_Lq_tsum_of_nonneg
+ summable_mul_rpow_of_Lp_Lq
++ Lr_rpow_le_Lp_mul_Lq
++ all_pos
- inner_le_Lp_mul_Lq_tsum_of_nonneg'

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.

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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-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.

[ADedecker]

Thanks, and sorry for the delay.

bors d+

[mathlib-bors]

✌️ j-loreaux can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[j-loreaux]

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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