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My question is really simple. I'm reading a book which states this theorem:

If $f:A_1\times A_2\to \mathbb R$ is integrable and $f$ is continuous then

$$\int_{A_1\times A_2}f(x,y)dxdy=\int_{A_1}dx\bigg(\int_{A_2}f(x,y)dy\bigg)=\int_{A_2}dy\bigg(\int_{A_1}f(x,y)dx\bigg)$$

Is this Fubini's theorem?

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    Fubini's Theorem cover a more general case. But yes. – 2017-01-29
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    It's a similar result to Fubini's theorem but has stronger assumptions (continuity is not required for the result to hold) https://en.wikipedia.org/wiki/Fubini's_theorem – 2017-01-29

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