Theorems · Theorem · probability
ProbabilityTheory.lintegral_exponentialPDF_of_nonpos
∀ {x r : ℝ}, x ≤ 0 → ∫⁻ (y : ℝ) in Set.Iio x, ProbabilityTheory.exponentialPDF r y = 0The Lebesgue integral of the exponential pdf over nonpositive reals equals 0
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- 1 results in Mathlib
- Foundations
- Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Set.Iiostatement · cited by 1,166
- MeasureTheory.lintegralstatement · cited by 1,152
- ProbabilityTheory.exponentialPDFstatement · cited by 7
- ProbabilityTheory.lintegral_gammaPDF_of_nonposproof · cited by 1
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- ProbabilityTheory.lintegral_exponentialPDF_eq_antiDerivproof · cited by 1