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)