Theorems · Theorem · measure theory
ENNReal.tsum_const_eq_top_of_ne_zero
∀ {α : Type u_4} [Infinite α] {c : ENNReal}, c ≠ 0 → ∑' (x : α), c = ⊤- Cited by
- 4 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- Finset.cardproof · cited by 2,327
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- tsumstatement and proof · cited by 1,148
- nsmul_eq_mulproof · cited by 369
- Infinitestatement and proof · cited by 352
- Finset.sum_constproof · cited by 254
Cited by4
Results whose statement or proof uses this declaration.
- ENNReal.finite_const_le_of_tsum_ne_topproof · cited by 2
- ENNReal.tsum_set_oneproof · cited by 1
- MeasureTheory.Measure.addHaar_eq_zero_of_disjoint_translates_auxproof · cited by 1
- Set.Infinite.meas_eq_topproof · cited by 0