Theorems · Theorem · measure theory
IntervalIntegrable.norm
∀ {E : Type u_5} [inst : NormedAddCommGroup E] {a b : ℝ} {μ : MeasureTheory.Measure ℝ} {f : ℝ → E},
IntervalIntegrable f μ a b → IntervalIntegrable (fun x => ‖f x‖) μ a b- Cited by
- 5 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Norm.normstatement · cited by 5,413
- IntervalIntegrablestatement and proof · cited by 316
- MeasureTheory.Integrable.normproof · cited by 63
Cited by5
Results whose statement or proof uses this declaration.
- intervalIntegral.continuousWithinAt_primitiveproof · cited by 6
- IntervalIntegrable.absproof · cited by 3
- hasSum_two_pi_I_cauchyPowerSeries_integralproof · cited by 2
- hasDerivAt_circleAverage_herglotzRieszKernel_smulproof · cited by 1
- not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter_auxproof · cited by 1