indepFun_div_left — Mathlib

English

If f i and f j are independent of f k for i ≠ k, then f i / f j is independent of f k.

Русский

Если f_i и f_j независимы от f_k при i ≠ k, то f_i / f_j независим от f_k.

LaTeX

$$$ \\operatorname{iIndepFun} f μ \\rightarrow \\forall i j k, i \\neq k \\rightarrow j \\neq k \\rightarrow \\operatorname{IndepFun} (instHDiv.hDiv (f i) (f j)) (f k) μ$$$

Lean4

@[to_additive]
theorem indepFun_div_left (hf_indep : iIndepFun f μ) (hf_meas : ∀ i, Measurable (f i)) (i j k : ι) (hik : i ≠ k)
    (hjk : j ≠ k) : IndepFun (f i / f j) (f k) μ :=
  Kernel.iIndepFun.indepFun_div_left hf_indep hf_meas i j k hik hjk

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