Theorems · Theorem · real analysis
integrable_one_add_norm
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E]
[inst_3 : MeasurableSpace E] [BorelSpace E] {μ : MeasureTheory.Measure E} [μ.IsAddHaarMeasure] {r : ℝ},
↑(Module.finrank ℝ E) < r → MeasureTheory.Integrable (fun x => (1 + ‖x‖) ^ (-r)) μ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealproof · cited by 9,879
- Top.topproof · cited by 9,680
- Norm.normstatement and proof · cited by 5,413
- Nat.cast_oneproof · cited by 2,501
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- BorelSpacestatement and proof · cited by 1,602
Cited by1
Results whose statement or proof uses this declaration.
- integrable_rpow_neg_one_add_norm_sqproof · cited by 2