innerRegularWRT_isCompact — Mathlib

English

For μ on a suitable space, InnerRegularWRT (IsCompact s ∧ IsClosed s) IsClosed is equivalent to InnerRegularWRT IsCompact IsClosed.

Русский

Для μ на подходящемSpace внутренности регулярен по IsCompact с замыканием и IsClosed.

LaTeX

$$$\\mu.InnerRegularWRT (\\text{IsCompact }\\circ \\text{closure}) IsClosed.$$$

Lean4

theorem innerRegularWRT_isCompact [UniformSpace α] [CompleteSpace α] [SecondCountableTopology α]
    [(uniformity α).IsCountablyGenerated] [OpensMeasurableSpace α] (P : Measure α) [IsFiniteMeasure P] :
    P.InnerRegularWRT IsCompact IsClosed :=
  by
  rw [← innerRegularWRT_isCompact_closure_iff]
  exact innerRegularWRT_isCompact_closure P

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