map_apply_eq_iff_map_symm_apply_eq

English

For a MeasurableEquiv e, μ.map e = ν if and only if μ = ν.map e.symm.

Русский

Для измеримого эквивалента e верно: μ.map e = ν тогда и только тогда, когда μ = ν.map e.symm.

LaTeX

$$$$\\forall e:\\alpha \\simeq\\beta,\\; \\mu.map e = \\nu \\iff \\mu = \\nu.map e^{-1}.$$$$

Lean4

theorem map_apply_eq_iff_map_symm_apply_eq (e : α ≃ᵐ β) : μ.map e = ν ↔ μ = ν.map e.symm := by
  rw [← (map_measurableEquiv_injective e).eq_iff, map_map_symm]

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