Theorems · Theorem · probability
ProbabilityTheory.lintegral_gammaPDF_of_nonpos
∀ {x a r : ℝ}, x ≤ 0 → ∫⁻ (y : ℝ) in Set.Iio x, ProbabilityTheory.gammaPDF a r y = 0The Lebesgue integral of the gamma pdf over nonpositive reals equals 0
- Defined in
- Mathlib.Probability.Distributions.Gamma
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 257 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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- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
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- 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_exponentialPDF_of_nonposproof · cited by 1