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Theorems · Theorem · measure theory

ENNReal.tsum_mul_left

∀ {α : Type u_1} {a : ENNReal} {f : α → ENNReal}, ∑' (i : α), a * f i = a * ∑' (i : α), f i
Defined in
Mathlib.Topology.Algebra.InfiniteSum.ENNReal
Cited by
21 results in Mathlib
Foundations
Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

ENNReal.tsum_mul_right · cited by 5ENNReal.tsum_mul_rightMeasureTheory.addHaar_image_le_mul_of_det_lt · cited by 4MeasureTheory.addHaar_ima…PMF.bind_bind · cited by 3PMF.bind_bindedist_le_of_edist_le_geometric_of_tendsto · cited by 3edist_le_of_edist_le_geom…cauchySeq_of_edist_le_geometric · cited by 2cauchySeq_of_edist_le_geo…PMF.toOuterMeasure_bind_apply · cited by 2PMF.toOuterMeasure_bind_a…MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux1 · cited by 1MeasureTheory.lintegral_a…ProbabilityTheory.Kernel.IndepSets.indep_aux · cited by 1IndepSets.indep_auxENNReal.tsum_geometric_add_one · cited by 1ENNReal.tsum_geometric_ad…Vitali.exists_disjoint_covering_ae · cited by 1Vitali.exists_disjoint_co…MeasureTheory.Egorov.measure_iUnionNotConvergentSeq · cited by 1Egorov.measure_iUnionNotC…MeasureTheory.Measure.exists_null_set_measure_lt_of_disjoint · cited by 1Measure.exists_null_set_m…ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mul · cited by 1Fernique.lintegral_exp_mu…MeasureTheory.OuterMeasure.smul_ofFunction · cited by 1OuterMeasure.smul_ofFunct…MeasureTheory.addHaar_image_eq_zero_of_det_fderivWithin_eq_zero_aux · cited by 1MeasureTheory.addHaar_ima…Finset · cited by 13712FinsetENNReal · cited by 9879ENNRealnhds · cited by 5554nhdsFinset.sum · cited by 5195Finset.sumFilter.Tendsto · cited by 3814Filter.TendstoFilter.atTop · cited by 2405Filter.atTopMulZeroClass.mul_zero · cited by 2091MulZeroClass.mul_zeroSummationFilter.unconditional · cited by 2068SummationFilter.unconditi…tsum · cited by 1148tsumSummable.hasSum · cited by 184Summable.hasSumHasSum.tsum_eq · cited by 150HasSum.tsum_eqtsum_zero · cited by 63tsum_zeroENNReal.summable · cited by 59ENNReal.summableENNReal.Tendsto.const_mul · cited by 13Tendsto.const_mulENNReal.tsum_eq_zero · cited by 3ENNReal.tsum_eq_zeroENNReal.tsum_mul_leftCITED BYCITES

Cites15

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

Cited by21

Results whose statement or proof uses this declaration.