of_measure_le_smul — Mathlib

English

If hT is dominated FinMeasAdditive for μ, then μ+ν inherits the bound with C.

Русский

Если hT доминированное FinMeasAdditive для μ, тогда μ+ν наследует границу с C.

LaTeX

$$add_measure_right μ ν hT hC$$

Lean4

theorem of_measure_le_smul {μ' : Measure α} {c : ℝ≥0∞} (hc : c ≠ ∞) (h : μ ≤ c • μ')
    (hT : DominatedFinMeasAdditive μ T C) (hC : 0 ≤ C) : DominatedFinMeasAdditive μ' T (c.toReal * C) :=
  (hT.of_measure_le h hC).of_smul_measure hc

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