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