instIsLocallyFiniteMeasure — Mathlib

English

If μ is locally finite, then the measure obtained by weighting ν with the Radon–Nikodym derivative μ with respect to ν is locally finite: ν.withDensity(μ.rnDer ν) is locally finite.

Русский

Если μ локально конечна, то мера, получаемая взвешиванием ν по радионовскому производному μ относительно ν, локально конечна: ν.withDensity(μ.rnDer ν) локально конечна.

LaTeX

$$$\\operatorname{IsLocallyFiniteMeasure}\\bigl(\\nu\\text{ withDensity }(\\mu\\mathrm{rnDer}\\nu)\\bigr)$$$

Lean4

instance instIsLocallyFiniteMeasure [TopologicalSpace α] [IsLocallyFiniteMeasure μ] :
    IsLocallyFiniteMeasure (ν.withDensity <| μ.rnDeriv ν) :=
  isLocallyFiniteMeasure_of_le <| withDensity_rnDeriv_le μ ν

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