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Theorems · Theorem · measure theory

AEMeasurable.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} {μ : MeasureTheory.Measure α} {f : α → β},
  AEMeasurable f μ → ∀ (c : γ), AEMeasurable (fun x => f x ^ c) μ
Defined in
Mathlib.MeasureTheory.Group.Arithmetic
Cited by
27 results in Mathlib
Foundations
Depth 176 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.

ProbabilityTheory.variance_eq_integral · cited by 10ProbabilityTheory.varianc…MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_norm · cited by 4MemLp.eLpNorm_eq_integral…MeasureTheory.eLpNorm_map_measure · cited by 3MeasureTheory.eLpNorm_map…MeasureTheory.eLpNorm_le_eLpNorm_top_mul_eLpNorm · cited by 3MeasureTheory.eLpNorm_le_…MeasureTheory.lpNorm_eq_integral_norm_rpow_toReal · cited by 3MeasureTheory.lpNorm_eq_i…MeasureTheory.MemLp.norm_rpow_div · cited by 2MemLp.norm_rpow_divMeasureTheory.MemLp.enorm_rpow_div · cited by 2MemLp.enorm_rpow_divMeasureTheory.pow_mul_meas_ge_le_eLpNorm · cited by 2MeasureTheory.pow_mul_mea…ENNReal.lintegral_Lp_mul_le_Lq_mul_Lr · cited by 2ENNReal.lintegral_Lp_mul_…MeasureTheory.ae_eq_zero_of_eLpNorm'_eq_zero · cited by 1MeasureTheory.ae_eq_zero_…MeasureTheory.eLpNorm'_le_mul_eLpNorm'_of_ae_le_mul · cited by 1MeasureTheory.eLpNorm'_le…MeasureTheory.Lp.eLpNorm'_lim_le_liminf_eLpNorm' · cited by 1Lp.eLpNorm'_lim_le_liminf…MeasureTheory.L2.eLpNorm_inner_lt_top · cited by 1L2.eLpNorm_inner_lt_topENNReal.lintegral_Lp_add_le_of_le_one · cited by 1ENNReal.lintegral_Lp_add_…ENNReal.ae_eq_zero_of_lintegral_rpow_eq_zero · cited by 1ENNReal.ae_eq_zero_of_lin…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureAEMeasurable · cited by 840AEMeasurableaemeasurable_const · cited by 22aemeasurable_constMeasurablePow · cited by 9MeasurablePowAEMeasurable.pow · cited by 4AEMeasurable.powAEMeasurable.pow_constCITED BYCITES

Cites6

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Cited by27

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