Theorems · Theorem · measure theory
MeasureTheory.setLIntegral_congr_fun
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → ENNReal} {s : Set α},
MeasurableSet s → Set.EqOn f g s → ∫⁻ (x : α) in s, f x ∂μ = ∫⁻ (x : α) in s, g x ∂μ- Cited by
- 31 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.lintegralstatement · cited by 1,152
- Set.EqOnstatement and proof · cited by 603
- Filter.Eventually.of_forallproof · cited by 526
- MeasureTheory.setLIntegral_congr_fun_aeproof · cited by 11
Cited by31
Results whose statement or proof uses this declaration.
- Manifold.pathELength_eq_lintegral_mfderivWithin_Iccproof · cited by 5
- MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_monotoneOnproof · cited by 3
- MeasureTheory.setLIntegral_eq_zeroproof · cited by 2
- ProbabilityTheory.lintegral_gammaPDF_eq_oneproof · cited by 2
- Manifold.pathELength_comp_of_monotoneOnproof · cited by 2
- Manifold.pathELength_congr_Iooproof · cited by 2
- lintegral_comp_pi_polarCoord_symmproof · cited by 1
- lintegral_comp_polarCoord_symmproof · cited by 1
- lintegral_fderiv_lineMap_eq_edistproof · cited by 1
- MeasureTheory.Integrable.integral_eq_integral_meas_ltproof · cited by 1
- ProbabilityTheory.Kernel.setIntegral_densityProcess_of_memproof · cited by 1