Theorems · Theorem · real analysis
enorm_sub_le_lintegral_deriv_of_contDiffOn_Icc
∀ {E : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : ℝ → E} {a b : ℝ},
ContDiffOn ℝ 1 f (Set.Icc a b) → a ≤ b → ‖f b - f a‖ₑ ≤ ∫⁻ (x : ℝ) in Set.Icc a b, ‖deriv f x‖ₑ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites52
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idproof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measureproof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- ENatstatement · cited by 4,985
- WithTopstatement · cited by 3,754
- LE.le.transproof · cited by 3,151
- Filter.Eventuallyproof · cited by 3,134
- MeasureTheory.aeproof · cited by 2,352
Cited by1
Results whose statement or proof uses this declaration.
- enorm_sub_le_lintegral_derivWithin_Icc_of_contDiffOn_Iccproof · cited by 1