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Theorems · Theorem · sequences and series

tsum_zero

∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] {L : SummationFilter β},
  ∑'[L] (x : β), 0 = 0
Defined in
Mathlib.Topology.Algebra.InfiniteSum.Basic
Cited by
63 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidTopologicalSpace

Around this declaration

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

tsum_mul_left · cited by 21tsum_mul_leftENNReal.tsum_mul_left · cited by 21ENNReal.tsum_mul_leftMeasureTheory.measure_biUnion_null_iff · cited by 11MeasureTheory.measure_biU…tsum_empty · cited by 6tsum_emptytsum_mul_right · cited by 6tsum_mul_rightProbabilityTheory.Kernel.sum_zero · cited by 6Kernel.sum_zeroMeasureTheory.Measure.nullSingletonClass_hausdorff · cited by 5Measure.nullSingletonClas…MeasureTheory.IsFundamentalDomain.measure_zero_of_invariant · cited by 4IsFundamentalDomain.measu…MeasureTheory.IsAddFundamentalDomain.measure_zero_of_invariant · cited by 4IsAddFundamentalDomain.me…tsum_const_smul'' · cited by 3tsum_const_smul''lp.norm_zero · cited by 3lp.norm_zeroSummable.tsum_pos · cited by 3Summable.tsum_posMeasureTheory.integral_tsum · cited by 3MeasureTheory.integral_ts…VitaliFamily.ae_eventually_measure_pos · cited by 3VitaliFamily.ae_eventuall…Real.ofDigits_le_one · cited by 3Real.ofDigits_le_oneSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceAddCommMonoid · cited by 12281AddCommMonoidSet.Finite · cited by 1814Set.Finitetsum · cited by 1148tsumSet.indicator · cited by 723Set.indicatorSummationFilter · cited by 607SummationFilterHasSum · cited by 518HasSumfinsum · cited by 286finsumSummationFilter.HasSupport · cited by 38SummationFilter.HasSupportSummationFilter.support · cited by 36SummationFilter.supportSet.empty_inter · cited by 30Set.empty_interfinsum_zero · cited by 18finsum_zerohasSum_zero · cited by 13hasSum_zerotsum_def · cited by 11tsum_deftsum_zeroCITED BYCITES

Cites19

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

Cited by63

Results whose statement or proof uses this declaration.