instMulAction — Mathlib

English

There is a scalar action of a monoid R on measures making (Measure α) into a MulAction; the action is defined via the outer measure and is compatible with injective embedding and smul-to-outer-measure.

Русский

Существует действие моноида R на мерах, превращающее (Measure α) в MulAction; действие задаётся через внешнюю меру и совместимо с внедрением и умножением во внешнюю меру.

LaTeX

$$$\text{MulAction } R\,(\text{Measure}(\alpha))$ with the action defined by $c \cdot \mu$ and compatible properties.$$

Lean4

instance instMulAction [Monoid R] [MulAction R ℝ≥0∞] [IsScalarTower R ℝ≥0∞ ℝ≥0∞] {_ : MeasurableSpace α} :
    MulAction R (Measure α) :=
  Injective.mulAction _ toOuterMeasure_injective smul_toOuterMeasure

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