Theorems · Theorem · functional analysis
lipschitzWith_smul
∀ {α : Type u_1} {β : Type u_2} [inst : SeminormedAddGroup α] [inst_1 : SeminormedAddGroup β]
[inst_2 : SMulZeroClass α β] [IsBoundedSMul α β] (s : α), LipschitzWith ‖s‖₊ fun x => s • x- Defined in
- Mathlib.Analysis.Normed.MulAction
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- NNNorm.nnnormstatement · cited by 952
- SeminormedAddGroupstatement and proof · cited by 331
- IsBoundedSMulstatement and proof · cited by 329
- LipschitzWithstatement · cited by 316
- SMulZeroClassstatement and proof · cited by 213
- lipschitzWith_iff_dist_le_mulproof · cited by 10
- dist_smul_leproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.hausdorffMeasure_smul₀proof · cited by 3
- edist_smul_leproof · cited by 1
- ediam_smul_leproof · cited by 1
- ediam_smul₀proof · cited by 1
- Bornology.IsBounded.smul₀proof · cited by 0