Theorems · Theorem · probability
ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_le_one
∀ {α : Type u_1} {f : α → ℚ → ℝ} [inst : MeasurableSpace α] (hf : ProbabilityTheory.IsMeasurableRatCDF f) (a : α)
(x : ℝ), ↑(hf.stieltjesFunction a) x ≤ 1- Cited by
- 2 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- MeasurableSpacestatement and proof · cited by 13,106
- Set.rangeproof · cited by 4,705
- iInfproof · cited by 1,690
- StieltjesFunction.toFunstatement · cited by 120
- ProbabilityTheory.IsMeasurableRatCDFstatement and proof · cited by 24
- ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionstatement and proof · cited by 11
- exists_rat_gtproof · cited by 10
- ciInf_le_of_leproof · cited by 8
- ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_eqproof · cited by 5
- ProbabilityTheory.IsMeasurableRatCDF.nonnegproof · cited by 3
- StieltjesFunction.iInf_rat_gt_eqproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atTopproof · cited by 3
- ProbabilityTheory.stieltjesOfMeasurableRat_le_oneproof · cited by 1