Theorems · Theorem · measure theory
IntervalIntegrable.const_mul
∀ {A : Type u_7} [inst : NormedRing A] {a b : ℝ} {μ : MeasureTheory.Measure ℝ} {f : ℝ → A},
IntervalIntegrable f μ a b → ∀ (c : A), IntervalIntegrable (fun x => c * f x) μ a b- Cited by
- 14 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- MeasureTheory.Measurestatement and proof · cited by 10,939
- NormedRingstatement and proof · cited by 924
- IntervalIntegrablestatement and proof · cited by 316
- continuousOn_constproof · cited by 96
- IntervalIntegrable.continuousOn_mulproof · cited by 8
Cited by14
Results whose statement or proof uses this declaration.
- MeromorphicOn.circleIntegrable_log_normproof · cited by 11
- MeromorphicOn.circleIntegrable_posLog_normproof · cited by 7
- intervalIntegral.intervalIntegrable_cpow'proof · cited by 7
- MeromorphicOn.intervalIntegrable_log_normproof · cited by 4
- Chebyshev.integral_theta_div_log_sq_isBigOproof · cited by 2
- CircleIntegrable.const_smulproof · cited by 2
- circleAverage_log_norm_factorizedRationalproof · cited by 1
- hasDerivAt_circleAverage_herglotzRieszKernel_smulproof · cited by 1
- Complex.betaIntegral_recurrenceproof · cited by 1
- ZetaAsymptotics.term_of_ltproof · cited by 1
- MeromorphicOn.intervalIntegrable_posLog_normproof · cited by 1
- IntervalIntegrable.intervalIntegrable_slopeproof · cited by 1