For given $σ, σ_1, σ_2, . . . ∈ L^d,$ ($L^d$ set of all signed measures) we should show that $\lim_{n}σ_n = σ ⇔ ∀A ∈ F, \; \lim_{n} σ_n(A) = σ(A).$

Question

For given $σ, σ_1, σ_2, . . . ∈ L^d,$ ($L^d$ set of all signed measures) we should show that $$\lim_{n}σ_n = σ ⇔ ∀A ∈ F, \; \lim_{n} σ_n(A) = σ(A).$$

I would appreciate any kind of help!