Theorems · Theorem · general topology
LocallyLipschitz.max
∀ {α : Type u} [inst : PseudoEMetricSpace α] {f g : α → ℝ},
LocallyLipschitz f → LocallyLipschitz g → LocallyLipschitz fun x => max (f x) (g x)The maximum of locally Lipschitz functions is locally Lipschitz.
- Defined in
- Mathlib.Topology.MetricSpace.Lipschitz
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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
- PseudoEMetricSpacestatement and proof · cited by 1,536
- LocallyLipschitzstatement and proof · cited by 34
- LipschitzWith.locallyLipschitzproof · cited by 6
- lipschitzWith_maxproof · cited by 3
- LocallyLipschitz.compproof · cited by 3
- LocallyLipschitz.prodMkproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- LocallyLipschitz.max_constproof · cited by 1