Theorems · Theorem · measure theory
MeasureTheory.FiniteMeasure.continuous_integral_boundedContinuousFunction
∀ {X : Type u_2} [inst : TopologicalSpace X] [inst_1 : MeasurableSpace X] [inst_2 : OpensMeasurableSpace X]
(f : BoundedContinuousFunction X ℝ), Continuous fun μ => ∫ (x : X), f x ∂↑μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- Continuousstatement · cited by 2,592
- MeasureTheory.integralstatement · cited by 1,779
- OpensMeasurableSpacestatement and proof · cited by 636
- BoundedContinuousFunctionstatement and proof · cited by 511
- continuous_idproof · cited by 192
- MeasureTheory.FiniteMeasurestatement · cited by 150
- MeasureTheory.FiniteMeasure.toMeasurestatement · cited by 87
- MeasureTheory.FiniteMeasure.continuous_iff_forall_continuous_integralproof · cited by 2
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