Slice symm measurable Embedding
Space.slice_symm_measurableEmbedding
Project documentation
The linear equivalence between Space d.succ and ℝ × Space d extracting the ith coordinate. -/ def slice {d} (i : Fin d.succ) : Space d.succ ≃L[ℝ] ℝ × Space d where toFun x := ⟨x i, ⟨fun j => x (Fin.succAbove i j)⟩⟩ invFun p := ⟨fun j => Fin.insertNthEquiv (fun _ => ℝ) i (p.fst, p.snd) j⟩ map_add' x y := by simp only [Nat.succ_eq_add_one, Prod.mk_add...
Exact Lean statement
lemma slice_symm_measurableEmbedding {d : ℕ} (i : Fin d.succ) :
MeasurableEmbedding (slice i).symmFormal artifact
Lean source
lemma slice_symm_measurableEmbedding {d : ℕ} (i : Fin d.succ) : MeasurableEmbedding (slice i).symm := by change MeasurableEmbedding (fun (p : ℝ × Space d) => (Space.equivPi d.succ).symm ((MeasurableEquiv.piFinSuccAbove (fun _ => ℝ) i).symm (p.fst, p.snd))) apply MeasurableEmbedding.comp · apply Measurable.measurableEmbedding · fun_prop · exact ContinuousLinearEquiv.injective (equivPi d.succ).symm apply MeasurableEmbedding.comp · exact MeasurableEquiv.measurableEmbedding (MeasurableEquiv.piFinSuccAbove (fun x => ℝ) i).symm · apply Measurable.measurableEmbedding · fun_prop · intro a b h match a, b with | (r1, x1), (r2, x2) => simp_all- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/SpaceAndTime/Space/Slice.lean:122-137
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