symmMeasurableEquiv — Mathlib

English

For the iUnion-type lemma, we have a bound on the content over a union of indexed cylinders by the sum over indices.

Русский

Для леммы iUnion имеем ограничение содержания на объединение цилиндров по индексам суммой содержания по индексам.

LaTeX

$$$\forall n,\ \operatorname{projectiveFamilyContent} hP (\bigcup_{i=0}^{n} s_i) \le \sum_{i=0}^{n} \operatorname{projectiveFamilyContent} hP (s_i)$$$

Lean4

/-- `unitInterval.symm` bundled as a measurable equivalence. -/
@[simps]
def symmMeasurableEquiv : I ≃ᵐ I where
  toFun := σ
  invFun := σ
  left_inv := symm_symm
  right_inv := symm_symm
  measurable_toFun := measurable_symm
  measurable_invFun := measurable_symm

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