Theorems · Theorem · real analysis
ENNReal.toReal_pos_iff
∀ {a : ENNReal}, 0 < a.toReal ↔ 0 < a ∧ a < ⊤- Defined in
- Mathlib.Data.ENNReal.Real
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement · cited by 9,680
- ENNReal.toRealstatement · cited by 859
- NNReal.coe_posproof · cited by 31
- ENNReal.toNNReal_pos_iffproof · cited by 2
Cited by20
Results whose statement or proof uses this declaration.
- ENNReal.toReal_posproof · cited by 59
- PiLp.norm_eq_sumproof · cited by 8
- lp.norm_eq_tsum_rpowproof · cited by 7
- WithLp.prod_norm_eq_addproof · cited by 6
- WithLp.prod_edist_eq_addproof · cited by 5
- ENNReal.log_mul_addproof · cited by 4
- PiLp.edist_eq_sumproof · cited by 4
- ENNReal.log_rpowproof · cited by 4
- memℓp_gen_iffproof · cited by 4
- MeasureTheory.eLpNorm_le_eLpNorm_mul_eLpNorm_of_nnnormproof · cited by 4
- ENNReal.HolderTriple.of_toRealproof · cited by 3
- MeasureTheory.eLpNorm_le_eLpNorm_top_mul_eLpNormproof · cited by 3