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Let f(x,y) be a function defined on the unit square $0\leq x\leq1$, $0\leq y\leq1$ that is continuous on each variable separately. Is f a measurable function of (x,y)?

I think I need to look at the pre-images of f, and I need to use the fact that it is continuous. Maybe I can use the epsilon-delta definition of continuous functions?

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    Satisfied with an answer below?2012-10-25

2 Answers 2