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Theorems · Theorem · commutative algebra

ENNReal.smul_def

∀ {M : Type u_1} [inst : MulAction ENNReal M] (c : NNReal) (x : M), c • x = ↑c • x
Defined in
Mathlib.Data.ENNReal.Action
Cited by
22 results in Mathlib
Foundations
Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MulAction
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.Measure.singularPart_smul · cited by 4Measure.singularPart_smulENNReal.toReal_smul · cited by 3ENNReal.toReal_smulENNReal.coe_smul · cited by 3ENNReal.coe_smulAddMonoidHom.measurePreserving · cited by 2AddMonoidHom.measurePrese…MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul · cited by 2MeasureTheory.eLpNorm'_le…HolderWith.smul · cited by 2HolderWith.smuleHolderNorm_smul · cited by 2eHolderNorm_smulMeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul' · cited by 2MeasureTheory.eLpNorm'_le…MeasureTheory.Lp.nnnorm_le_of_ae_bound · cited by 2Lp.nnnorm_le_of_ae_boundMeasureTheory.Measure.singularPart_smul_right · cited by 2Measure.singularPart_smul…MeasureTheory.Measure.rnDeriv_smul_right · cited by 2Measure.rnDeriv_smul_rightMonoidHom.measurePreserving · cited by 2MonoidHom.measurePreservi…MeasureTheory.le_eLpNorm_of_bddBelow · cited by 1MeasureTheory.le_eLpNorm_…ediam_smul₀ · cited by 1ediam_smul₀MeasureTheory.Lp.nnnorm_le_mul_nnnorm_of_ae_le_mul · cited by 1Lp.nnnorm_le_mul_nnnorm_o…ENNReal · cited by 9879ENNRealNNReal · cited by 4310NNRealMulAction · cited by 1294MulActionENNReal.ofNNReal · cited by 1279ENNReal.ofNNRealENNReal.smul_defCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by22

Results whose statement or proof uses this declaration.