Theorems · Theorem · measure theory
MeasureTheory.integral_sub_right_eq_self
∀ {G : Type u_4} {E : Type u_5} [inst : MeasurableSpace G] [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E]
{μ : MeasureTheory.Measure G} [inst_3 : AddGroup G] [MeasurableAdd G] [μ.IsAddRightInvariant] (f : G → E) (g : G),
∫ (x : G), f (x - g) ∂μ = ∫ (x : G), f x ∂μ- Defined in
- Mathlib.MeasureTheory.Group.Integral
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddGroupstatement and proof · cited by 4,410
- MeasureTheory.integralstatement and proof · cited by 1,779
- sub_eq_add_negproof · cited by 1,023
- MeasurableAddstatement and proof · cited by 78
- MeasureTheory.Measure.IsAddRightInvariantstatement and proof · cited by 59
- MeasureTheory.integral_add_right_eq_selfproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.Integrable.convolution_integrandproof · cited by 6
- ProbabilityTheory.integral_cauchyPDFReal_eq_oneproof · cited by 2
- ProbabilityTheory.lintegral_gaussianPDFReal_eq_oneproof · cited by 2
- Real.fourier_bilin_convolution_eq_integralproof · cited by 1
- MeasureTheory.convolution_assoc'proof · cited by 1
- MeasureTheory.integral_convolutionproof · cited by 1