Theorems · Theorem · real analysis
ENNReal.sum_lt_top
∀ {α : Type u_1} {s : Finset α} {f : α → ENNReal}, ∑ a ∈ s, f a < ⊤ ↔ ∀ a ∈ s, f a < ⊤A sum is finite iff all summands are finite.
- Defined in
- Mathlib.Data.ENNReal.BigOperators
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement · cited by 9,680
- Finset.sumstatement · cited by 5,195
- WithTop.sum_lt_topproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.measure_support_lt_topproof · cited by 3
- ENNReal.lt_top_of_sum_ne_topproof · cited by 2
- MeasureTheory.SimpleFunc.memLp_of_finite_measure_preimageproof · cited by 1
- MeasureTheory.SimpleFunc.FinMeasSupp.lintegral_lt_topproof · cited by 1
- MeasureTheory.Measure.MeasureDense.of_generateFrom_isSetAlgebra_finiteproof · cited by 1