I want to prove that the following function $g(x,y)=\int_{t=0}^{t=x-y} f(y,t)dt$ is continuous in x and y on $[0,1]^2$ where I assume that the function f(y,t) is continuous in y and t, nonnegative and bounded. I looked for a specific theorems that could help me in proving this, but didn't succeed to find something useful. Now I think that it would be best to prove it directly with an $\epsilon-\delta$ proof. However, this is also not straightforward and I'm still struggling to find the proof. Does somebody know of any theorem out there that could be useful to this problem? Or does somebody know how to directly prove this? I really appreciate all the help! Thank you in advance!
2026-04-01 16:21:32.1775060492
Proving continuity of two variable function with integral
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