Theorems · Theorem · real analysis
ENNReal.div_le_iff_le_mul
∀ {a b c : ENNReal}, b ≠ 0 ∨ c ≠ ⊤ → b ≠ ⊤ ∨ c ≠ 0 → (a / b ≤ c ↔ a ≤ c * b)- Defined in
- Mathlib.Data.ENNReal.Inv
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 136 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.
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- div_eq_mul_invproof · cited by 715
- inv_invproof · cited by 494
- ENNReal.le_div_iff_mul_leproof · cited by 15
Cited by10
Results whose statement or proof uses this declaration.
- ENNReal.div_le_of_le_mulproof · cited by 10
- MeasureTheory.Measure.hausdorffMeasure_zero_or_topproof · cited by 3
- VitaliFamily.ae_tendsto_divproof · cited by 2
- VitaliFamily.measure_le_mul_of_subset_limRatioMeas_ltproof · cited by 2
- ENNReal.lt_div_iff_mul_ltproof · cited by 1
- bergelson'proof · cited by 1
- egauge_smul_rightproof · cited by 1
- MeasureTheory.Integrable.uniformIntegrable_condExpproof · cited by 1
- ENNReal.inv_le_iff_le_mulproof · cited by 1
- VitaliFamily.exists_measurable_supersets_limRatioproof · cited by 1