Theorems · Theorem · special functions
integrable_exp_neg_mul_sq
∀ {b : ℝ}, 0 < b → MeasureTheory.Integrable (fun x => Real.exp (-b * x ^ 2)) MeasureTheory.volume- Cited by
- 6 results in Mathlib
- Foundations
- Depth 285 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
- one_mulproof · cited by 2,841
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Real.expstatement and proof · cited by 871
- neg_mulproof · cited by 654
- Real.rpow_zeroproof · cited by 69
- integrable_rpow_mul_exp_neg_mul_sqproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- ProbabilityTheory.integrable_gaussianPDFRealproof · cited by 4
- integrableOn_Ioi_exp_neg_mul_sq_iffproof · cited by 2
- integrable_cexp_neg_mul_sqproof · cited by 2
- continuousAt_gaussian_integralproof · cited by 1
- GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_Iproof · cited by 1
- integrable_exp_neg_mul_sq_iffproof · cited by 0