toENNRealVectorMeasure — Mathlib

English

The congruence lemma for the additive commutative group instance holds; equality transfers along isomorphisms in the additive structure.

Русский

Лемма конгруэнтности для инстанса AddCommGroup сохраняет равенство через изоморфизмы в аддитивной структуре.

LaTeX

$$$\text{instAddCommGroup}.congr_simp$$$

Lean4

/-- A measure is a vector measure over `ℝ≥0∞`. -/
@[simps]
def toENNRealVectorMeasure (μ : Measure α) : VectorMeasure α ℝ≥0∞
    where
  measureOf' := fun i : Set α => if MeasurableSet i then μ i else 0
  empty' := by simp
  not_measurable' _ hi := if_neg hi
  m_iUnion' _ hf₁
    hf₂ :=
    by
    rw [Summable.hasSum_iff ENNReal.summable, if_pos (MeasurableSet.iUnion hf₁), MeasureTheory.measure_iUnion hf₂ hf₁]
    exact tsum_congr fun n => if_pos (hf₁ n)

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