Theorems · Theorem · real analysis
ENNReal.toReal_eq_zero_iff
∀ (x : ENNReal), x.toReal = 0 ↔ x = 0 ∨ x = ⊤
- Defined in
- Mathlib.Data.ENNReal.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 and proof · cited by 9,680
- ENNReal.toRealstatement · cited by 859
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.measureReal_eq_zero_iffproof · cited by 9
- ENNReal.toReal_ne_zeroproof · cited by 5
- MeasureTheory.condExp_bot'proof · cited by 3
- MeasureTheory.mul_meas_ge_le_pow_eLpNormproof · cited by 3
- Set.infsep_zeroproof · cited by 2
- MeasureTheory.continuous_L1_toL1proof · cited by 1
- MeasureTheory.Integrable.integral_eq_integral_Ioc_meas_leproof · cited by 1
- variationOnFromTo.eq_zero_iff_of_geproof · cited by 1
- variationOnFromTo.eq_zero_iff_of_leproof · cited by 1