ofMeasurableSpace — Mathlib

English

The Has part of a generated Dynkin system equals GenerateHas: (generate C).Has = GenerateHas C.

Русский

Элемент Has порожденной Dynkin-системы совпадает с GenerateHas: (generate C).Has = GenerateHas C.

LaTeX

$$$\mathrm{(generate\ C).Has} = \mathrm{GenerateHas}\ C$$$

Lean4

/-- Every measurable space (σ-algebra) forms a Dynkin system -/
def ofMeasurableSpace (m : MeasurableSpace α) : DynkinSystem α
    where
  Has := m.MeasurableSet'
  has_empty := m.measurableSet_empty
  has_compl {a} := m.measurableSet_compl a
  has_iUnion_nat {f} _ hf := m.measurableSet_iUnion f hf

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