Mathlib Map

Theorems · Theorem · real analysis

ENNReal.mul_iSup

∀ {ι : Sort u_1} (a : ENNReal) (f : ι → ENNReal), a * ⨆ i, f i = ⨆ i, a * f i
Defined in
Mathlib.Data.ENNReal.Inv
Cited by
13 results in Mathlib
Foundations
Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

MeasureTheory.lintegral_const_mul · cited by 19MeasureTheory.lintegral_c…MeasureTheory.lintegral_iSup · cited by 16MeasureTheory.lintegral_i…MeasureTheory.lintegral_withDensity_eq_lintegral_mul · cited by 5MeasureTheory.lintegral_w…ENNReal.iSup_mul · cited by 5ENNReal.iSup_mulHolderOnWith.hausdorffMeasure_image_le · cited by 2HolderOnWith.hausdorffMea…ENNReal.smul_iSup · cited by 2ENNReal.smul_iSupMeasureTheory.lintegral_const_mul_le · cited by 2MeasureTheory.lintegral_c…MeasureTheory.Measure.InnerRegularWRT.smul · cited by 2InnerRegularWRT.smulAntilipschitzWith.hausdorffMeasure_preimage_le · cited by 2AntilipschitzWith.hausdor…ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace · cited by 1ProbabilityTheory.lintegr…MeasureTheory.SimpleFunc.lintegral_restrict_iUnion_of_directed · cited by 1SimpleFunc.lintegral_rest…MeasureTheory.Submartingale.mul_lintegral_upcrossings_le_lintegral_pos_part · cited by 1Submartingale.mul_lintegr…ENNReal.mul_sSup · cited by 1ENNReal.mul_sSupENNReal · cited by 9879ENNRealTop.top · cited by 9680Top.topiSup · cited by 2415iSupMulZeroClass.mul_zero · cited by 2091MulZeroClass.mul_zeroMulZeroClass.zero_mul · cited by 1625MulZeroClass.zero_muleq_or_ne · cited by 1117eq_or_neIff.not · cited by 489Iff.notEq.ge · cited by 375Eq.geTop · cited by 93Tople_iSup_of_le · cited by 79le_iSup_of_leENNReal.top_mul · cited by 29ENNReal.top_mulOrderIso.map_iSup · cited by 25OrderIso.map_iSupENNReal.iSup_zero · cited by 15ENNReal.iSup_zeroENNReal.mulLeftOrderIso · cited by 5ENNReal.mulLeftOrderIsoENNReal.iSup_eq_zero · cited by 3ENNReal.iSup_eq_zeroENNReal.mul_iSupCITED BYCITES

Cites16

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

Cited by13

Results whose statement or proof uses this declaration.