Theorems · Theorem · measure theory
MeasureTheory.setLIntegral_congr
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal} {s t : Set α},
s =ᵐ[μ] t → ∫⁻ (x : α) in s, f x ∂μ = ∫⁻ (x : α) in t, f x ∂μ- Cited by
- 11 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- MeasureTheory.Measure.restrict_congr_setproof · cited by 43
Cited by11
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_monotoneOnproof · cited by 3
- NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integralproof · cited by 2
- MeasureTheory.withDensity_apply₀proof · cited by 2
- NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integralproof · cited by 1
- MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image₀proof · cited by 1
- lintegral_comp_pi_polarCoord_symmproof · cited by 1
- lintegral_comp_polarCoord_symmproof · cited by 1
- ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mulproof · cited by 1
- NumberField.mixedEmbedding.lintegral_comp_polarCoordReal_symmproof · cited by 1
- MeasureTheory.setLAverage_congrproof · cited by 0