instIsInvInvariantCount — Mathlib

English

If μ is left-invariant on G and f: G →* H is a measurable embedding, then (μ.comap f) is left-invariant.

Русский

Если μ слева инвариантна на G и f: G →* H — измеримое вложение, то (μ.comap f) слева инвариантна.

LaTeX

$$$ (\mu .comap f) \text{ is left-invariant}$, i.e. $ (\mu .comap f)(gA) = (\mu .comap f)(A) $ for all $g \in G$ and measurable $A$.$$

Lean4

@[to_additive]
instance : (count : Measure G).IsInvInvariant where
  inv_eq_self := by ext s hs; rw [count_apply hs, inv_apply, count_apply hs.inv, encard_inv]

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