fpvandoorn/carleson
Source indexedtheorem · leanprover/lean4:v4.32.0
MeasureTheory.lintegral_comp_eq_lintegral_distribution_mul'
Carleson.ToMathlib.MeasureTheory.Integral.Layercake · Carleson/ToMathlib/MeasureTheory/Integral/Layercake.lean:479 to 490
Mathematical statement
Exact Lean statement
theorem lintegral_comp_eq_lintegral_distribution_mul' (μ : Measure α)
(f_mble : AEMeasurable f μ) (g_mble : AEMeasurable g) :
∫⁻ ω, (∫⁻ t in (Iio (f ω)), g t) ∂μ =
∫⁻ t, distribution f t μ * g tComplete declaration
Lean source
Full Lean sourceLean 4
theorem lintegral_comp_eq_lintegral_distribution_mul' (μ : Measure α) (f_mble : AEMeasurable f μ) (g_mble : AEMeasurable g) : ∫⁻ ω, (∫⁻ t in (Iio (f ω)), g t) ∂μ = ∫⁻ t, distribution f t μ * g t := by rcases f_mble with ⟨fF, hF, f_eq_F⟩ convert lintegral_comp_eq_lintegral_distribution_mul μ hF g_mble using 1 · apply lintegral_congr_ae filter_upwards [f_eq_F] with ω hω congr · congr with t congr 1 apply distribution_congr_ae f_eq_F