Theorems · Theorem · real analysis
ENNReal.toReal_le_of_le_ofReal
∀ {a : ENNReal} {b : ℝ}, 0 ≤ b → a ≤ ENNReal.ofReal b → a.toReal ≤ b- Defined in
- Mathlib.Data.ENNReal.Real
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- ENNReal.ofRealstatement and proof · cited by 863
- ENNReal.toRealstatement · cited by 859
- ne_top_of_le_ne_topproof · cited by 68
- ENNReal.ofReal_ne_topproof · cited by 34
- ENNReal.le_ofReal_iff_toReal_leproof · cited by 11
Cited by14
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.densityProcess_le_oneproof · cited by 5
- Metric.diam_le_of_forall_dist_leproof · cited by 5
- MeasureTheory.norm_indicatorConstLp_leproof · cited by 2
- ProbabilityTheory.Kernel.rnDerivAux_le_oneproof · cited by 2
- Besicovitch.card_le_of_separatedproof · cited by 2
- MeasureTheory.measureReal_le_oneproof · cited by 1
- MeasureTheory.tendsto_Lp_finite_of_tendsto_ae_of_measproof · cited by 1
- ProbabilityTheory.isRatCondKernelCDFAux_preCDFproof · cited by 1
- MeasureTheory.levyProkhorovDist_le_of_forall_leproof · cited by 1
- BoxIntegral.unitPartition.diam_boxIccproof · cited by 1
- Metric.hausdorffDist_le_of_infDistproof · cited by 1
- ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_ge_leproof · cited by 1