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feat(MeasureTheory/Integral): add integrableOn_of_integrableOn_inter_support #37590

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feat(MeasureTheory/Integral): add integrableOn_of_integrableOn_inter_support #37590

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6 changes: 6 additions & 0 deletions Mathlib/MeasureTheory/Integral/IntegrableOn.lean
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Expand Up @@ -431,6 +431,12 @@ theorem IntegrableOn.of_forall_diff_eq_zero {f : α → ε'}
(h't : ∀ x ∈ t \ s, f x = 0) : IntegrableOn f t μ :=
hf.of_ae_diff_eq_zero ht.nullMeasurableSet (Eventually.of_forall h't)

theorem integrableOn_of_integrableOn_inter_support {f : α → ε'}
(hs : MeasurableSet s) (hf : IntegrableOn f (s ∩ support f) μ) :
IntegrableOn f s μ := by
apply IntegrableOn.of_forall_diff_eq_zero hf hs
simp

/-- If a function is integrable on a set `s` and vanishes almost everywhere on its complement,
then it is integrable. -/
theorem IntegrableOn.integrable_of_ae_notMem_eq_zero
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