singularPart_singularPart — Mathlib

English

The singular part of μ with respect to ν, when further decomposed by ν, remains μ.singularPart ν.

Русский

Сингулярная часть μ по ν, затем again по ν, сохраняет μ.singularPart ν.

LaTeX

$$$$ (μ.singularPart ν).singularPart ν = μ.singularPart ν $$$$

Lean4

@[simp]
theorem singularPart_singularPart (μ ν : Measure α) : (μ.singularPart ν).singularPart ν = μ.singularPart ν :=
  by
  rw [Measure.singularPart_eq_self]
  exact Measure.mutuallySingular_singularPart _ _

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