Let (X,FX),(Y,FY),(Z,FZ) be measurable spaces. Let f:(X,FX)→(Y,FY) and g:(Y,FY)→(Z,FZ) be measurable functions. Then we have that their composition g∘f:(X,FX)→(Z,FZ)is also measurable.
Again, like in the definition of measurable functions we can generalize this theorem to deal with topological spaces
Let (X,M) be a measurable space, let (Y,TY),(Z,TZ) be topological spaces. Let f:X→Y be measurable and let g:Y→Z be continuous, then: h=g∘f:X→Z is measurable