Theorems · Theorem · ordinary differential equations

ODE.FunSpace.intervalIntegrable_comp_compProj

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [NormedSpace ℝ E] {f : ℝ → E → E} {tmin tmax : ℝ}
  {t₀ : ↑(Set.Icc tmin tmax)} {x₀ : E} {a r L K : NNReal},
  IsPicardLindelof f t₀ x₀ a r L K →
    ∀ (α : ODE.FunSpace t₀ x₀ r L) (t : ↑(Set.Icc tmin tmax)),
      IntervalIntegrable (fun t' => f t' (α.compProj t')) MeasureTheory.volume ↑t₀ ↑t

The integrand in next is integrable.

Defined in: Mathlib.Analysis.ODE.PicardLindelof
Cited by: 1 results in Mathlib
Foundations: Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
NormedSpacestatement and proof · cited by 12,499
Set.Elemstatement and proof · cited by 7,166
NNRealstatement and proof · cited by 4,310
Set.Iccstatement and proof · cited by 1,702
MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
IntervalIntegrablestatement · cited by 316
ContinuousOn.monoproof · cited by 156
ODE.FunSpacestatement and proof · cited by 37
IsPicardLindelofstatement and proof · cited by 33

Cited by1

Results whose statement or proof uses this declaration.

ODE.FunSpace.dist_iterate_next_apply_leproof · cited by 1