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This commit is contained in:
Stefan Kebekus 2024-08-02 12:46:21 +02:00
parent 03548bc6da
commit 103fd5fb0f
1 changed files with 44 additions and 0 deletions

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@ -392,8 +392,52 @@ theorem primitive_additivity
unfold primitive unfold primitive
have integrability₁
(a₁ a₂ b : ) :
IntervalIntegrable (fun x => f { re := x, im := b }) MeasureTheory.volume a₁ a₂ := by
apply ContinuousOn.intervalIntegrable
apply ContinuousOn.comp
exact hf.continuousOn
have : ((fun x => { re := x, im := b }) : ) = (fun x => Complex.ofRealCLM x + { re := 0, im := b }) := by
funext x
apply Complex.ext
rw [Complex.add_re]
simp
rw [Complex.add_im]
simp
apply Continuous.continuousOn
rw [this]
continuity
--
intro w hw
simp
rw [Complex.dist_eq_re_im]
have : (∫ (x : ) in z₀.re..z.re, f { re := x, im := z₀.im }) = (∫ (x : ) in z₀.re..z₁.re, f { re := x, im := z₀.im }) + (∫ (x : ) in z₁.re..z.re, f { re := x, im := z₀.im }) := by have : (∫ (x : ) in z₀.re..z.re, f { re := x, im := z₀.im }) = (∫ (x : ) in z₀.re..z₁.re, f { re := x, im := z₀.im }) + (∫ (x : ) in z₁.re..z.re, f { re := x, im := z₀.im }) := by
rw [intervalIntegral.integral_add_adjacent_intervals] rw [intervalIntegral.integral_add_adjacent_intervals]
-- IntervalIntegrable (fun x => f { re := x, im := z₀.im }) MeasureTheory.volume z₀.re z₁.re
apply ContinuousOn.intervalIntegrable
apply ContinuousOn.comp
exact hf.continuousOn
have {b : } : ((fun x => { re := x, im := b }) : ) = (fun x => Complex.ofRealCLM x + { re := 0, im := b }) := by
funext x
apply Complex.ext
rw [Complex.add_re]
simp
rw [Complex.add_im]
simp
apply Continuous.continuousOn
rw [this]
continuity
-- Remains: Set.MapsTo (fun x => { re := x, im := z₀.im }) (Set.uIcc z₀.re z₁.re) (Metric.ball z₀ R)
intro w hw
simp
sorry --apply integrability₁ f hf sorry --apply integrability₁ f hf
sorry --apply integrability₁ f hf sorry --apply integrability₁ f hf
rw [this] rw [this]