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Theorems · Theorem · complex analysis

CircleIntegrable.const_smul

∀ {c : ℂ} {R : ℝ} {A : Type u_2} [inst : NormedRing A] {a : A} {f : ℂ → A},
  CircleIntegrable f c R → CircleIntegrable (a • f) c R

If f is circle integrable, then so are its scalar multiples.

Defined in
Mathlib.MeasureTheory.Integral.CircleIntegral
Cited by
2 results in Mathlib
Foundations
Depth 244 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedRing
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Around this declaration

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

circleIntegrable_log_norm_factorizedRational · cited by 1circleIntegrable_log_norm…CircleIntegrable.const_fun_smul · cited by 0CircleIntegrable.const_fu…Real · cited by 25697RealComplex · cited by 5565ComplexNormedRing · cited by 924NormedRingCircleIntegrable · cited by 86CircleIntegrableIntervalIntegrable.const_mul · cited by 14IntervalIntegrable.const_…CircleIntegrable.const_smulCITED BYCITES

Cites5

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Cited by2

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