Theorems · Theorem · real analysis
ENNReal.toReal_mono
∀ {a b : ENNReal}, b ≠ ⊤ → a ≤ b → a.toReal ≤ b.toReal- Defined in
- Mathlib.Data.ENNReal.Real
- Cited by
- 59 results in Mathlib
- Foundations
- Depth 110 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 and proof · cited by 9,680
- ENNReal.toRealstatement · cited by 859
- ne_top_of_le_ne_topproof · cited by 68
- ENNReal.toReal_le_toRealproof · cited by 17
Cited by59
Results whose statement or proof uses this declaration.
- Metric.infDist_le_dist_of_memproof · cited by 13
- MeasureTheory.MemLp.mono_exponentproof · cited by 11
- ENNReal.toNNReal_monoproof · cited by 10
- Metric.diam_monoproof · cited by 7
- MeasureTheory.measureReal_monoproof · cited by 5
- MeasureTheory.lpNorm_add_leproof · cited by 5
- MeasureTheory.DominatedFinMeasAdditive.of_measure_leproof · cited by 4
- MeasureTheory.measureReal_union_leproof · cited by 4
- MeasureTheory.eLpNorm_add_le'proof · cited by 3
- SchwartzMap.denseRange_toLpCLMproof · cited by 3
- MeasureTheory.eLpNorm_le_eLpNorm_mul_rpow_measure_univproof · cited by 3
- ProbabilityTheory.Kernel.setIntegral_densityproof · cited by 2