Theorems · Theorem · measure theory
MeasureTheory.FiniteMeasure.average_eq_integral_normalize
∀ {Ω : Type u_1} [inst : Nonempty Ω] {m0 : MeasurableSpace Ω} (μ : MeasureTheory.FiniteMeasure Ω) {E : Type u_2}
[inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E],
μ ≠ 0 → ∀ (f : Ω → E), MeasureTheory.average (↑μ) f = ∫ (ω : Ω), f ω ∂↑μ.normalizeAveraging with respect to a finite measure is the same as integrating against
MeasureTheory.FiniteMeasure.normalize.
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- Foundations
- Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound
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- ENNReal.ofNNRealproof · cited by 1,279
- MeasureTheory.FiniteMeasurestatement and proof · cited by 150
- MeasureTheory.FiniteMeasure.toMeasurestatement and proof · cited by 87
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