Theorems · Theorem · measure theory
intervalIntegral.integral_const
∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b : ℝ} [CompleteSpace E] (c : E),
∫ (x : ℝ) in a..b, c = (b - a) • c- Cited by
- 33 results in Mathlib
- Foundations
- Depth 256 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.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- CompleteSpacestatement and proof · cited by 2,532
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- ENNReal.ofRealproof · cited by 863
- ENNReal.toRealproof · cited by 859
- intervalIntegralstatement · cited by 546
- neg_subproof · cited by 272
- Real.volume_Iocproof · cited by 11
- intervalIntegral.integral_const'proof · cited by 3
- max_zero_sub_eq_selfproof · cited by 2
Cited by33
Results whose statement or proof uses this declaration.
- Real.circleAverage_constproof · cited by 9
- Real.circleAverage_zeroproof · cited by 6
- Polynomial.Chebyshev.integral_eval_T_real_measureT_zeroproof · cited by 3
- AntitoneOn.integral_le_sumproof · cited by 3
- AntitoneOn.sum_le_integralproof · cited by 2
- integral_cos_sqproof · cited by 2
- sum_Ico_le_integral_of_leproof · cited by 2
- MeasureTheory.lintegral_eq_lintegral_meas_leproof · cited by 2
- circleIntegral.integral_sub_center_invproof · cited by 2
- Polynomial.logMahlerMeasure_constproof · cited by 2
- qExpansion_coeff_isBigO_of_norm_isBigOproof · cited by 2
- integral_sin_pow_evenproof · cited by 2