Theorems · Theorem · functional analysis
nnnorm_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
- 10 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement · cited by 952
- SeminormedAddGroupstatement and proof · cited by 331
- IsBoundedSMulstatement and proof · cited by 329
- SMulZeroClassstatement and proof · cited by 213
- norm_smul_leproof · cited by 24
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNorm_smul_le_mul_eLpNormproof · cited by 4
- Memℓp.const_smulproof · cited by 3
- MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_topproof · cited by 1
- ContinuousMultilinearMap.nnnorm_smulRightproof · cited by 1
- lp.norm_const_smul_leproof · cited by 1
- enorm_smul_leproof · cited by 1
- MeasureTheory.eLpNorm'_const_smul_leproof · cited by 1
- MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNormproof · cited by 0
- ContinuousLinearMap.opNNNorm_lsmul_apply_leproof · cited by 0
- MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm'proof · cited by 0