support_smul — Mathlib

English

For any set s, function r, and function f, the indicator of the smoothed product equals the smoothed product of the indicators.

Русский

Для любого множества s каждый индикатор смешанного произведения равен произведению индикаторов.

LaTeX

$$$ \operatorname{indicator}(s, \lambda a . r(a) \cdot f(a)) = (a \mapsto r(a)) \cdot \operatorname{indicator}(s, f) $$$

Lean4

theorem support_smul [Zero R] [Zero M] [SMulWithZero R M] [NoZeroSMulDivisors R M] (f : α → R) (g : α → M) :
    support (f • g) = support f ∩ support g :=
  ext fun _ => smul_ne_zero_iff

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