rnDeriv_singularPart — Mathlib

English

The RN-derivative of the singular part is almost surely zero: (μ.singularPart ν).rnDer ν =ᵐ[ν] 0.

Русский

Плотность РН операторa сингулярной части равна почти surely нулю: (μ.singularPart ν).rnDer ν =ᵐ[ν] 0.

LaTeX

$$$$ (μ.singularPart ν).rnDer ν =ᵐ[ν] 0 $$$$

Lean4

theorem rnDeriv_singularPart (μ ν : Measure α) : (μ.singularPart ν).rnDeriv ν =ᵐ[ν] 0 :=
  by
  rw [rnDeriv_eq_zero]
  exact mutuallySingular_singularPart μ ν

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