Theorems · Theorem · measure theory
MeasureTheory.setIntegral_univ
∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
{f : X → E} {μ : MeasureTheory.Measure X}, ∫ (x : X) in Set.univ, f x ∂μ = ∫ (x : X), f x ∂μ- Cited by
- 25 results in Mathlib
- Foundations
- Depth 250 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.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.univstatement · cited by 3,945
- MeasureTheory.integralstatement and proof · cited by 1,779
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.Measure.restrict_univproof · cited by 76
Cited by25
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_condExpproof · cited by 5
- MeasureTheory.integral_add_compl₀proof · cited by 4
- MeasureTheory.integral_of_hasDerivAt_of_tendstoproof · cited by 4
- ProbabilityTheory.Kernel.integral_densityproof · cited by 3
- integral_comp_polarCoord_symmproof · cited by 2
- MeasureTheory.integral_tiltedproof · cited by 2
- MeasureTheory.setIntegral_supportproof · cited by 2
- MeasureTheory.Measure.integral_toReal_rnDerivproof · cited by 2
- MeasureTheory.Integrable.tendsto_ae_condExpproof · cited by 2
- MeasureTheory.ae_eq_zero_of_forall_setIntegral_isClosed_eq_zeroproof · cited by 1
- MeasureTheory.measure_unitBall_eq_integral_div_gammaproof · cited by 1
- MeasureTheory.Submartingale.sum_mul_upcrossingStrat_leproof · cited by 1