HardyLittlewood.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL: Lean4 Domain Explanation Language

Annotation provenance. This overlay contains 10 curated AI-written annotations and 981 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Pinned Carleson blueprint

16 declarations, 0 contain sorry, 0 declared as axioms

This should roughly contain the contents of chapter 9.

Imports (3)

Imported by 5 files

lemma indicator_rpow line 54 source
lemma maximalFunction_eq_maximalFunction_one_rpow line 58 source
def T line 64 source
lemma T.add_le line 70 source
lemma NNReal.smul_ennreal_eq_mul move to ENNReal.Basic or similar line 77 source
Source comment
move to `ENNReal.Basic` or similar
```
lemma NNReal.smul_ennreal_eq_mul (x : ℝ≥0) (y : ℝ≥0∞) : x • y = x * y := rfl
```
lemma T.smul line 79 source
theorem measure_biUnion_le_lintegral_aux line 88 source
def tr line 124 source
lemma tr_mono line 126 source
lemma tr_union line 131 source
theorem MeasureTheory.MemLp.maximalFunction_lt_top line 186 source
theorem hasStrongType_maximalFunction_top line 196 source

theorem hasWeakType_maximalFunction_one The proof is roughly between (9.0.12)-(9.0.22) line 204 source

Source comment

The proof is roughly between (9.0.12)-(9.0.22).

theorem hasWeakType_maximalFunction_one [TopologicalSpace ε] [BorelSpace X] [SeparableSpace X] :
    HasWeakType (maximalFunction (ε := ε) μ 𝓑 c r 1) 1 1 μ μ (A ^ 2) := by
…

Mentions: c, A

theorem sublinearOn_maximalFunction_one line 229 source
theorem hasWeakType_maximalFunction_equal_exponents line 320 source
theorem maximalFunction_ae_lt_top line 379 source