isMulRightInvariant_smul_nnreal — Mathlib

English

If f is measure-preserving from μ' to μ and μ is left-invariant, then (g • f) is measure-preserving from μ' to μ.

Русский

Если fPreserving мера между μ' и μ, и μ инвариантна слева, то g • f сохраняет меры.

LaTeX

$$$\\text{MeasurePreserving}(f, \\mu', \\mu) \\Rightarrow \\text{MeasurePreserving}(g \\cdot f, \\mu', \\mu)$$$

Lean4

@[to_additive MeasureTheory.isAddRightInvariant_smul_nnreal]
instance isMulRightInvariant_smul_nnreal [IsMulRightInvariant μ] (c : ℝ≥0) : IsMulRightInvariant (c • μ) :=
  MeasureTheory.isMulRightInvariant_smul (c : ℝ≥0∞)

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