Theorems · Theorem · measure theory
MeasureTheory.setLIntegral_univ
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} (f : α → ENNReal),
∫⁻ (x : α) in Set.univ, f x ∂μ = ∫⁻ (x : α), f x ∂μ- Cited by
- 23 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Set.univstatement · cited by 3,945
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- MeasureTheory.Measure.restrict_univproof · cited by 76
Cited by23
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.lintegral_rnDeriv_lt_topproof · cited by 9
- MeasureTheory.withDensity_eq_iffproof · cited by 6
- MeasureTheory.lintegral_eq_lintegral_of_isPiSystem_of_univ_memproof · cited by 1
- lintegral_comp_polarCoord_symmproof · cited by 1
- lintegral_comp_pi_polarCoord_symmproof · cited by 1
- MeasureTheory.Measure.lintegral_rnDerivproof · cited by 1
- MeasureTheory.pdf.lintegral_eq_measure_univproof · cited by 1
- MeasureTheory.Measure.compProd_eq_zero_iffproof · cited by 1
- MeasureTheory.ae_eq_of_setLIntegral_prod_eqproof · cited by 1
- ProbabilityTheory.rnDeriv_posterior_ae_prodproof · cited by 1
- ProbabilityTheory.lintegral_stieltjesOfMeasurableRatproof · cited by 1
- ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mulproof · cited by 1