When I go through the proof of Riesz-Markov Representation Theorem
I could encounter a step of defining
$A_k=K\cap f^{-1}((y_k,y_{k+1}))$
$U_k=V\cap f^{-1}((y_k,y_{k+1}))$
And the $A_k\in \mathcal B$ which is Borel sigma algebra, how it is?? And How we can explain this by drawing a suitable diagram? Give me a suitable function to explain geometrically.