Theorems · Theorem · functional analysis
MeasureTheory.Measure.integrable_pow_neg_integrablePower
∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : MeasurableSpace E] (μ : MeasureTheory.Measure E)
[h : μ.HasTemperateGrowth], MeasureTheory.Integrable (fun x => (1 + ‖x‖) ^ (-↑μ.integrablePower)) μ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Norm.normstatement and proof · cited by 5,413
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- zpow_natCastproof · cited by 271
- zpow_negproof · cited by 198
- MeasureTheory.Measure.HasTemperateGrowthstatement and proof · cited by 41
- Real.rpow_neg_natCastproof · cited by 5
- MeasureTheory.Measure.integrablePowerstatement · cited by 5
- MeasureTheory.Measure.HasTemperateGrowth.exists_integrableproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- integral_pow_mul_le_of_le_of_pow_mul_leproof · cited by 1
- integrable_of_le_of_pow_mul_leproof · cited by 1