Theorems · Theorem · probability
ProbabilityTheory.lintegral_paretoPDF_of_le
∀ {t r x : ℝ}, x ≤ t → ∫⁻ (y : ℝ) in Set.Iio x, ProbabilityTheory.paretoPDF t r y = 0The Lebesgue integral of the Pareto pdf over reals ≤ t equals 0.
- Defined in
- Mathlib.Probability.Distributions.Pareto
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 243 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- ENNRealstatement and proof · cited by 9,879
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- Set.Iiostatement and proof · cited by 1,166
- MeasureTheory.lintegralstatement · cited by 1,152
- ENNReal.ofRealproof · cited by 863
- ENNReal.ofReal_zeroproof · cited by 56
- MeasureTheory.setLIntegral_congr_funproof · cited by 31
- MeasureTheory.lintegral_zeroproof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.lintegral_paretoPDF_eq_oneproof · cited by 1