Theorems · Theorem · measure theory

MeasureTheory.integral_norm_eq_pos_sub_neg

∀ {X : Type u_1} {mX : MeasurableSpace X} {μ : MeasureTheory.Measure X} {f : X → ℝ},
  MeasureTheory.Integrable f μ →
    ∫ (x : X), ‖f x‖ ∂μ = ∫ (x : X) in {x | 0 ≤ f x}, f x ∂μ - ∫ (x : X) in {x | f x ≤ 0}, f x ∂μ

Defined in: Mathlib.MeasureTheory.Integral.Bochner.Set
Cited by: 1 results in Mathlib
Foundations: Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound

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

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Cited by1

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MeasureTheory.integral_norm_le_of_forall_fin_meas_integral_eqproof · cited by 1