Theorems · Theorem · functional analysis
nnnorm_smul
∀ {α : Type u_1} {β : Type u_2} [inst : SeminormedRing α] [inst_1 : SeminormedAddGroup β] [inst_2 : SMul α β]
[NormSMulClass α β] (r : α) (x : β), ‖r • x‖₊ = ‖r‖₊ * ‖x‖₊- Defined in
- Mathlib.Analysis.Normed.MulAction
- Cited by
- 14 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.
Cites7
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
- SeminormedRingstatement and proof · cited by 446
- SeminormedAddGroupstatement and proof · cited by 331
- norm_smulproof · cited by 242
- NNReal.eqproof · cited by 201
- NormSMulClassstatement and proof · cited by 107
Cited by14
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.exists_lt_apply_of_lt_opNNNormproof · cited by 3
- Module.Basis.opNNNorm_leproof · cited by 2
- MeasureTheory.setLIntegral_nnnorm_condExpIndSMul_leproof · cited by 2
- MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_leproof · cited by 2
- Bornology.IsVonNBounded.restrict_scalars_of_nontrivialproof · cited by 1
- ContinuousLinearMap.exists_nnnorm_eq_one_lt_apply_of_lt_opNNNormproof · cited by 1
- spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smulproof · cited by 1
- ContinuousMap.nnnorm_smul_constproof · cited by 1
- ContinuousMultilinearMap.nnnorm_smulRightproof · cited by 1
- MeasureTheory.VectorMeasure.variation_transpose_lsmulproof · cited by 0
- MeasureTheory.VectorMeasure.variation_transpose_lsmul_flipproof · cited by 0
- RCLike.nnnorm_nnqsmulproof · cited by 0