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Theorems · Theorem · special functions

Real.Gamma_pos_of_pos

∀ {s : ℝ}, 0 < s → 0 < Real.Gamma s
Defined in
Mathlib.Analysis.SpecialFunctions.Gamma.Basic
Cited by
17 results in Mathlib
Foundations
Depth 282 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Real.convexOn_log_Gamma · cited by 5Real.convexOn_log_GammaReal.Gamma_ne_zero · cited by 3Real.Gamma_ne_zeroProbabilityTheory.beta_pos · cited by 2ProbabilityTheory.beta_posReal.convexOn_Gamma · cited by 2Real.convexOn_GammaProbabilityTheory.lintegral_gammaPDF_eq_one · cited by 2ProbabilityTheory.lintegr…Real.deriv_Gamma_nat · cited by 2Real.deriv_Gamma_natReal.Gamma_three_div_two_lt_one · cited by 2Real.Gamma_three_div_two_…ProbabilityTheory.gammaPDFReal_nonneg · cited by 2ProbabilityTheory.gammaPD…MeasureTheory.measure_unitBall_eq_integral_div_gamma · cited by 1MeasureTheory.measure_uni…Real.BohrMollerup.tendsto_log_gamma · cited by 1BohrMollerup.tendsto_log_…Real.Gamma_mul_Gamma_add_half_of_pos · cited by 1Real.Gamma_mul_Gamma_add_…Real.doublingGamma_eq_Gamma · cited by 1Real.doublingGamma_eq_Gam…Real.eq_Gamma_of_log_convex · cited by 1Real.eq_Gamma_of_log_conv…intervalIntegral_pow_mul_exp_neg_le · cited by 1intervalIntegral_pow_mul_…ProbabilityTheory.gammaPDFReal_pos · cited by 1ProbabilityTheory.gammaPD…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetReal · cited by 25697RealENNReal · cited by 9879ENNRealTop.top · cited by 9680Top.topLT.lt.le · cited by 2189lt.leSet.Ioi · cited by 1463Set.IoiLT.lt.ne' · cited by 1417lt.ne'MeasureTheory.MeasureSpace.volume · cited by 1323MeasureSpace.volumeReal.exp · cited by 871Real.expFunction.support · cited by 610Function.supportmul_pos · cited by 374mul_posmul_ne_zero · cited by 178mul_ne_zeroReal.exp_pos · cited by 169Real.exp_posReal.rpow_pos_of_pos · cited by 155Real.rpow_pos_of_posReal.Gamma_pos_of_posCITED BYCITES

Cites27

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by17

Results whose statement or proof uses this declaration.