measurable_real_toNNReal — Mathlib

English

If two locally finite measures μ,ν on R agree on all open intervals Ioo with rational endpoints, then μ = ν.

Русский

Если две locally-finite меры μ, ν на ℝ согласованы на все открытые интервалы Ioo с рациональными границами, то μ = ν.

LaTeX

$$$\\\\forall μ ν : \\\\mathrm{Measure}(\\\\mathbb{R}), [\\\\operatorname{IsLocallyFiniteMeasure} μ], [\\\\operatorname{IsLocallyFiniteMeasure} ν], (\\\\forall a,b \\\\in \\\\mathbb{Q}, μ(Ioo(a,b)) = ν(Ioo(a,b))) \\\\Rightarrow μ = ν$$$

Lean4

@[measurability, fun_prop]
theorem measurable_real_toNNReal : Measurable Real.toNNReal :=
  continuous_real_toNNReal.measurable

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