I started working on a problema on building a sequence of continuous function whose pointwise limit has to be a real valued function f. I mean: $f:R^2 \rightarrow [-\infty; +\infty]$ and I know that the two function fixing the single variables defined as:
h:$t \rightarrow f(x,t)$
g:$t \rightarrow f(t,y)$
are continuous. I'm asked to prove that f is the pointwise limit of a sequence of continuous function (and since it is proved it also measurable).
So I started working with the variables y fixed;imaging that if I consider f for each $(x,y+\frac{1}{2^n})$ the succesion $f_n=f(x,y+\frac{1}{2^n})$.
I can get that this tends to f (using the conitinuity of g) but $f_n$ as defined is not continuous.So I don't know how to solve this problem.May I use some difference between two points as continuous function (where the continuity is given by the functions g and h)? I'm in lack if ideas..