I am working my way through the title "Lebesgue Integration on Euclidean Space" by Frank Jones. On page 25 there is a definition for special rectangles. Is there a constraint on these type of rectangles to be parallel to the axis (seems so from the following figure in the book)? If not, what is the definition for these rectangles?
I could not find any good definition online. All I could find is examples like a square. Must a square be parallel to the axis?
Note, the definition for the rectangle is as follows: $$ I=[a_1,b_1 ]×⋯×[a_n,b_n ]=\{x∈\mathbb R^n |a_i≤x_i≤b_i for 1≤i≤n\}$$