closure_paramSet_ae_interior — Mathlib

English

The ae-equivalence holds for the closure and interior of paramSet under the measure volume.

Русский

ae-эквивалентность для замыкания иInterior paramSet относительно объёма.

LaTeX

$$closure(paramSet K) =ᵐ[volume] interior(paramSet K)$$

Lean4

theorem closure_paramSet_ae_interior : closure (paramSet K) =ᵐ[volume] interior (paramSet K) :=
  by
  rw [closure_paramSet, interior_paramSet, volume_pi]
  refine Measure.ae_eq_set_pi fun w _ ↦ ?_
  split_ifs
  · exact Iio_ae_eq_Iic.symm
  · exact Ioo_ae_eq_Icc.symm

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