Here's the problem:
Let X = (X1, X2, X3) be a vector of measurable real valued functions defined on a measurable space (Ω, F). Define function Y (ω, t) : Ω × R :→ R by setting Y (ω, t) = X1(ω)t$^2$ + X2(ω)t + X3(ω). Show that the mapping Y is F ⊗ B(R)/B(R) measurable.
I know that each function itself is measurable on (Ω, F) since each member of the vector is measurable, so X1, X2, and X3 each map from Ω to F. I'm just not sure how to show that it's measurable on F ⊗ B(R)/B(R), where F ⊗ B(R) is the product algebra. Very confused, any help is appreciated!