toFiniteAux — Mathlib

English

For AEMeasurable f,g: G→ℝ≥0∞, μ.withDensity f ∗ μ.withDensity g = μ.withDensity (f ⋆_{μ} g).

Русский

Для AEMeasurable f,g: G→ℝ≥0∞, μ.withDensity f ∗ μ.withDensity g = μ.withDensity (f ⋆_{μ} g).

LaTeX

$$$ μ^{f} *_{μ} μ^{g} = μ^{(f \star_{μ} g)} $$$

Lean4

/-- Auxiliary definition for `MeasureTheory.Measure.toFinite`. -/
noncomputable def toFiniteAux (μ : Measure α) [SFinite μ] : Measure α :=
  letI := Classical.dec
  if IsFiniteMeasure μ then μ else (exists_isFiniteMeasure_absolutelyContinuous μ).choose

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