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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 t

Complete declaration

Lean source

Canonical 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