Let n > 1 and let E⊂Rn be a line segment, where we use coordinates of x and y with respect to a fixed Cartesian coordinate system. Let ε > 0. Prove that there is a finite union of boxes I, where all boxes are defined using the same Cartesian coordinate system, such that E ⊆ I and v(I) < ε. Then show that A is Jordan measurable and v(E) = 0.
I thought about finding the longest edge of the box and then dividing this equally however im unsure on how this would work and where to go from there. Any help is appreciated thanks.