Theorems · Theorem · measure theory
IntervalIntegrable.mono_set
∀ {ε : Type u_3} [inst : TopologicalSpace ε] [inst_1 : ENormedAddMonoid ε] {f : ℝ → ε} {a b c d : ℝ}
{μ : MeasureTheory.Measure ℝ} [TopologicalSpace.PseudoMetrizableSpace ε],
IntervalIntegrable f μ a b → Set.uIcc c d ⊆ Set.uIcc a b → IntervalIntegrable f μ c d- Cited by
- 5 results in Mathlib
- Foundations
- Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- MeasureTheory.Measurestatement and proof · cited by 10,939
- le_rflproof · cited by 1,558
- Set.uIccstatement and proof · cited by 393
- IntervalIntegrablestatement and proof · cited by 316
- TopologicalSpace.PseudoMetrizableSpacestatement and proof · cited by 245
- ENormedAddMonoidstatement and proof · cited by 67
- IntervalIntegrable.monoproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- intervalIntegral.continuousWithinAt_primitiveproof · cited by 6
- intervalIntegral.integral_deriv_smul_comp'''proof · cited by 4
- Function.Periodic.intervalIntegrableproof · cited by 2
- MonotoneOn.intervalIntegral_slope_leproof · cited by 1
- IntervalIntegrable.intervalIntegrable_slopeproof · cited by 1