Definition Of A Double Integral

Hello,

I am currently reading about the preliminary work used to define the double integral, and there is one thing my author states, whose meaning I am not certain I understand. Here is an excerpt:

"The rectangles lying entirely within form an inner partition whose norm is defined as the length of the longest diagonal of the rectangles."

Could someone possibly explain the meaning of this to me, especially the part about the longest diagonal?

Thank you in advanced!

Re: Definition Of A Double Integral

It means that the rectangles in the partition doesn't have to be all of the same size, so their diagonals will be different. When the limit will be taken, to smaller rectangles will also tend to "zero"