Theorems · Theorem · measure theory
MeasureTheory.setIntegral_const
∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
{s : Set X} {μ : MeasureTheory.Measure X} [CompleteSpace E] (c : E), ∫ (x : X) in s, c ∂μ = μ.real s • c- Cited by
- 15 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- 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
- CompleteSpacestatement and proof · cited by 2,532
- MeasureTheory.integralstatement · cited by 1,779
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.Measure.realstatement and proof · cited by 530
- MeasureTheory.integral_constproof · cited by 75
- MeasureTheory.measureReal_restrict_apply_univproof · cited by 6
Cited by15
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_prodproof · cited by 9
- MeasureTheory.integral_indicator_constproof · cited by 7
- ProbabilityTheory.integral_compProdproof · cited by 4
- MeasureTheory.ae_nonneg_of_forall_setIntegral_nonnegproof · cited by 3
- intervalIntegral.integral_const'proof · cited by 3
- Filter.Tendsto.integral_sub_linear_isLittleO_aeproof · cited by 3
- tendsto_card_div_pow_atTop_volumeproof · cited by 2
- ae_eq_const_or_exists_average_ne_complproof · cited by 2
- norm_sub_le_mul_volume_of_norm_deriv_le_of_leproof · cited by 1
- MeasureTheory.norm_integral_sub_setIntegral_leproof · cited by 1
- MeasureTheory.condExp_indep_eqproof · cited by 1
- ProbabilityTheory.Kernel.integral_compproof · cited by 1