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 โโฅ0} :
MemLorentz (โ(algebraMap โ ๐) โ toReal โ f) p q ฮผ โ MemLorentz f p q ฮผComplete declaration
Lean source
Full Lean sourceLean 4
theorem memLorentz_iff_memLorentz_embedRCLike {๐ : Type*} [RCLike ๐] {f : ฮฑ โ โโฅ0} : MemLorentz (โ(algebraMap โ ๐) โ toReal โ 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