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fpvandoorn/carleson
Source indexedtheorem ยท leanprover/lean4:v4.32.0

MeasureTheory.memLorentz_iff_memLorentz_embedRCLike

Carleson.ToMathlib.LorentzType ยท Carleson/ToMathlib/LorentzType.lean:435 to 454

Mathematical statement

Exact Lean statement

theorem memLorentz_iff_memLorentz_embedRCLike {๐•‚ : Type*} [RCLike ๐•‚] {f : ฮฑ โ†’ โ„โ‰ฅ0} :
    MemLorentz (โ‡‘(algebraMap โ„ ๐•‚) โˆ˜ toReal โˆ˜ f) p q ฮผ โ†” MemLorentz f p q ฮผ

Complete declaration

Lean source

Canonical source
Full Lean sourceLean 4
theorem memLorentz_iff_memLorentz_embedRCLike {๐•‚ : Type*} [RCLike ๐•‚] {f : ฮฑ โ†’ โ„โ‰ฅ0} :    MemLorentz (โ‡‘(algebraMap โ„ ๐•‚) โˆ˜ toReal โˆ˜ f) p q ฮผ โ†” MemLorentz f p q ฮผ := by  constructor  ยท intro hf    constructor    ยท have := hf.1      rwa [aestronglyMeasurable_iff_aestronglyMeasurable_embedRCLike] at this    ยท convert hf.2 using 1      apply eLorentzNorm_congr_enorm_ae      apply Eventually.of_forall      intro x      symm      apply enorm_eq_enorm_embedRCLike  ยท intro hf    constructor    ยท have := hf.1      rwa [aestronglyMeasurable_iff_aestronglyMeasurable_embedRCLike]    ยท convert hf.2 using 1      apply eLorentzNorm_congr_enorm_ae      apply Eventually.of_forall enorm_eq_enorm_embedRCLike