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Theorems · Theorem · measure theory

Measurable.pow_const

∀ {β : Type u_2} {γ : Type u_3} {α : Type u_4} [inst : MeasurableSpace β] [inst_1 : MeasurableSpace γ]
  [inst_2 : Pow β γ] [MeasurablePow β γ] {m : MeasurableSpace α} {f : α → β},
  Measurable f → ∀ (c : γ), Measurable fun x => f x ^ c
Defined in
Mathlib.MeasureTheory.Group.Arithmetic
Cited by
26 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpaceMeasurableSpacePowMeasurablePow

Around this declaration

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

MeasureTheory.SimpleFunc.tendsto_approxOn_Lp_eLpNorm · cited by 3SimpleFunc.tendsto_approx…ProbabilityTheory.measurable_gammaPDFReal · cited by 3ProbabilityTheory.measura…ProbabilityTheory.measurable_uncurry_gaussianPDFReal · cited by 3ProbabilityTheory.measura…integrable_rpow_neg_one_add_norm_sq · cited by 2integrable_rpow_neg_one_a…ProbabilityTheory.measurable_cauchyPDFReal · cited by 2ProbabilityTheory.measura…Polynomial.Chebyshev.integrable_measureT · cited by 2Chebyshev.integrable_meas…ProbabilityTheory.measurable_paretoPDFReal · cited by 2ProbabilityTheory.measura…hasSum_two_pi_I_cauchyPowerSeries_integral · cited by 2hasSum_two_pi_I_cauchyPow…ProbabilityTheory.moment_truncation_eq_intervalIntegral_of_nonneg · cited by 2ProbabilityTheory.moment_…ProbabilityTheory.IdentDistrib.sq · cited by 1IdentDistrib.sqProbabilityTheory.measurable_betaPDFReal · cited by 1ProbabilityTheory.measura…MeasureTheory.ae_bdd_liminf_atTop_rpow_of_eLpNorm_bdd · cited by 1MeasureTheory.ae_bdd_limi…ProbabilityTheory.lintegral_betaPDF_eq_one · cited by 1ProbabilityTheory.lintegr…Polynomial.Chebyshev.integral_measureT · cited by 1Chebyshev.integral_measur…MeasureTheory.eLpNorm'_trim · cited by 1MeasureTheory.eLpNorm'_tr…MeasurableSpace · cited by 13106MeasurableSpaceMeasurable · cited by 1499Measurablemeasurable_const · cited by 156measurable_constMeasurablePow · cited by 9MeasurablePowMeasurable.pow · cited by 3Measurable.powMeasurable.pow_constCITED BYCITES

Cites5

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Cited by26

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