setToL1_lipschitz — Mathlib

English

SetToL1 is Lipschitz with constant C^{+}, namely ||setToL1 hT|| ≤ ||setToL1SCLM hT|| and the operator has Lipschitz bound with Real to NNReal.

Русский

SetToL1 обладает липшицевой ограниченностью: ||setToL1 hT|| ≤ ||setToL1SCLM hT||.

LaTeX

$$$\text{LipschitzWith} (\mathbb{R}_{+}\text{Real}) (setToL1 h_T) = ...$$$

Lean4

theorem setToL1_lipschitz (hT : DominatedFinMeasAdditive μ T C) : LipschitzWith (Real.toNNReal C) (setToL1 hT) :=
  (setToL1 hT).lipschitz.weaken (norm_setToL1_le' hT)

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