Theorems · Theorem · measure theory
intervalIntegral.integral_zero
∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b : ℝ} {μ : MeasureTheory.Measure ℝ},
∫ (x : ℝ) in a..b, 0 ∂μ = 0- Cited by
- 16 results in Mathlib
- Foundations
- Depth 253 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.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- sub_selfproof · cited by 996
- intervalIntegralstatement · cited by 546
- MeasureTheory.integral_zeroproof · cited by 59
Cited by16
Results whose statement or proof uses this declaration.
- Polynomial.logMahlerMeasure_eq_log_MahlerMeasureproof · cited by 4
- circleIntegral.integral_radius_zeroproof · cited by 3
- MeromorphicOn.circleAverage_log_normproof · cited by 3
- curveIntegral_reflproof · cited by 2
- taylor_integral_remainder_auxproof · cited by 2
- curveIntegral_zeroproof · cited by 1
- MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurableproof · cited by 1
- Polynomial.logMahlerMeasure_oneproof · cited by 1
- Polynomial.logMahlerMeasure_zeroproof · cited by 1
- MonotoneOn.intervalIntegral_slope_leproof · cited by 1
- Polynomial.logMahlerMeasure_Xproof · cited by 0