Theorems · Theorem · real analysis
ENNReal.iSup_eq_zero
∀ {ι : Sort u_1} {f : ι → ENNReal}, ⨆ i, f i = 0 ↔ ∀ (i : ι), f i = 0- Defined in
- Mathlib.Data.ENNReal.Operations
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- iSupstatement · cited by 2,415
- iSup_eq_botproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- ENNReal.mul_iSupproof · cited by 13
- eVariationOn.eq_zero_iffproof · cited by 3
- ContinuousLinearMap.eq_zero_of_forall_hasEigenvalue_eq_zeroproof · cited by 1