Theorems · Theorem · functional analysis
norm_smul_le
∀ {α : Type u_1} {β : Type u_2} [inst : SeminormedAddGroup α] [inst_1 : SeminormedAddGroup β]
[inst_2 : SMulZeroClass α β] [IsBoundedSMul α β] (r : α) (x : β), ‖r • x‖ ≤ ‖r‖ * ‖x‖- Defined in
- Mathlib.Analysis.Normed.MulAction
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 97 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.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- Dist.distproof · cited by 1,539
- smul_zeroproof · cited by 665
- SeminormedAddGroupstatement and proof · cited by 331
- IsBoundedSMulstatement and proof · cited by 329
- SMulZeroClassstatement and proof · cited by 213
- dist_zero_rightproof · cited by 172
- dist_zeroproof · cited by 16
- dist_smul_pairproof · cited by 5
Cited by24
Results whose statement or proof uses this declaration.
- nnnorm_smul_leproof · cited by 10
- MeasureTheory.DominatedFinMeasAdditive.smulproof · cited by 5
- isBoundedBilinearMap_smulproof · cited by 5
- FormalMultilinearSeries.radius_le_smulproof · cited by 3
- Asymptotics.IsBigOWith.smulproof · cited by 3
- Memℓp.const_smulproof · cited by 3
- PadicInt.norm_mahlerTermproof · cited by 2
- MeasureTheory.Integrable.smul_prodproof · cited by 2
- Asymptotics.IsBigOWith.const_smul_selfproof · cited by 2
- MeasureTheory.volume_sum_rpow_lt_oneproof · cited by 2
- Filter.Tendsto.zero_smul_isBoundedUnder_leproof · cited by 1
- MeasureTheory.StronglyMeasurable.norm_approxBounded_leproof · cited by 1