Theorems · Theorem · real analysis
ENNReal.prod_inv_distrib
∀ {ι : Type u_1} {f : ι → ENNReal} {s : Finset ι},
((↑s).Pairwise fun i j => f i ≠ 0 ∨ f j ≠ ⊤) → (∏ i ∈ s, f i)⁻¹ = ∏ i ∈ s, (f i)⁻¹- Defined in
- Mathlib.Data.ENNReal.BigOperators
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- SetLike.coestatement and proof · cited by 8,199
- Finset.prodstatement and proof · cited by 2,356
- Set.Pairwisestatement and proof · cited by 321
- inv_oneproof · cited by 301
- Finset.consproof · cited by 221
- Finset.cons_inductionproof · cited by 85
- Finset.prod_consproof · cited by 60
- Set.Pairwise.monoproof · cited by 55
- Finset.prod_ne_zero_iffproof · cited by 45
Cited by3
Results whose statement or proof uses this declaration.
- ENNReal.prod_div_distribproof · cited by 2
- ProbabilityTheory.cond_iInterproof · cited by 1
- ProbabilityTheory.Kernel.iIndepFun.cond_iInterproof · cited by 0