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- Cited by
- 63 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommMonoidstatement and proof · cited by 12,281
- Set.Finiteproof · cited by 1,814
- tsumstatement · cited by 1,148
- Set.indicatorproof · cited by 723
- SummationFilterstatement and proof · cited by 607
- HasSumproof · cited by 518
- finsumproof · cited by 286
- SummationFilter.HasSupportproof · cited by 38
- SummationFilter.supportproof · cited by 36
- Set.empty_interproof · cited by 30
Cited by63
Results whose statement or proof uses this declaration.
- tsum_mul_leftproof · cited by 21
- ENNReal.tsum_mul_leftproof · cited by 21
- MeasureTheory.measure_biUnion_null_iffproof · cited by 11
- tsum_emptyproof · cited by 6
- tsum_mul_rightproof · cited by 6
- ProbabilityTheory.Kernel.sum_zeroproof · cited by 6
- MeasureTheory.Measure.nullSingletonClass_hausdorffproof · cited by 5
- MeasureTheory.IsFundamentalDomain.measure_zero_of_invariantproof · cited by 4
- MeasureTheory.IsAddFundamentalDomain.measure_zero_of_invariantproof · cited by 4
- tsum_const_smul''proof · cited by 3
- lp.norm_zeroproof · cited by 3
- Summable.tsum_posproof · cited by 3