Theorems · Theorem · real analysis
intervalIntegral.intervalIntegrable_cpow
∀ {a b : ℝ} {μ : MeasureTheory.Measure ℝ} [MeasureTheory.IsLocallyFiniteMeasure μ] {r : ℂ},
0 ≤ r.re ∨ 0 ∉ Set.uIcc a b → IntervalIntegrable (fun x => ↑x ^ r) μ a bSee intervalIntegrable_cpow' for a version with a weaker hypothesis on r, but assuming the
measure is volume.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites55
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Top.topproof · cited by 9,680
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- Compl.complproof · cited by 2,925
- one_mulproof · cited by 2,841
- LT.lt.leproof · cited by 2,189
- Real.piproof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Set.Iooproof · cited by 1,214
Cited by2
Results whose statement or proof uses this declaration.
- integral_cpowproof · cited by 5
- integral_rpowproof · cited by 4