Theorems · Theorem · real analysis
ENNReal.prod_ne_top
∀ {α : Type u_1} {s : Finset α} {f : α → ENNReal}, (∀ a ∈ s, f a ≠ ⊤) → ∏ a ∈ s, f a ≠ ⊤A product of finite numbers is still finite.
- Defined in
- Mathlib.Data.ENNReal.BigOperators
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 120 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 and proof · cited by 9,680
- Finset.prodstatement · cited by 2,356
- WithTop.prod_ne_topproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- ENNReal.prod_inv_distribproof · cited by 3
- ProbabilityTheory.iCondIndepSets_iffproof · cited by 2
- ENNReal.tendsto_finsetProd_of_ne_topproof · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.volume_normLeOneproof · cited by 2
- MeasureTheory.integrable_comp_evalproof · cited by 1
- ENNReal.prod_rpow_of_ne_topproof · cited by 0