Theorems · Theorem · measure theory

BoundedContinuousFunction.integrable_of_nnreal

∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : MeasurableSpace X] (μ : MeasureTheory.Measure X)
  [MeasureTheory.IsFiniteMeasure μ] [OpensMeasurableSpace X] (f : BoundedContinuousFunction X NNReal),
  MeasureTheory.Integrable (NNReal.toReal ∘ ⇑f) μ

Defined in: Mathlib.MeasureTheory.Integral.BoundedContinuousFunction
Cited by: 0 results in Mathlib
Foundations: Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace MeasurableSpace MeasureTheory.IsFiniteMeasure OpensMeasurableSpace

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

DFunLike.coestatement and proof · cited by 62,936
Realstatement · cited by 25,697
TopologicalSpacestatement and proof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Top.topproof · cited by 9,680
NNRealstatement and proof · cited by 4,310
MeasureTheory.Integrablestatement · cited by 1,367
NNReal.toRealstatement · cited by 1,260
MeasureTheory.lintegralproof · cited by 1,152
MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
OpensMeasurableSpacestatement and proof · cited by 636

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