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## Main Question or Discussion Point

Hi, I need help getting a start on this exercise.

Let R be the unit square.

Find sequence of partitions such that the mesh size goes to zero as sequence goes to infinity -> for this, is this just a series of sub rectangles whose respective areas shrink at the same rate with respect to one another?

Find a sequence of partitions such that the max area of a sub rectangle tends to 0 while the mesh size of partition does not tend to zero as the limit approaches infinity of sequence of partitions.

Let R be the unit square.

Find sequence of partitions such that the mesh size goes to zero as sequence goes to infinity -> for this, is this just a series of sub rectangles whose respective areas shrink at the same rate with respect to one another?

Find a sequence of partitions such that the max area of a sub rectangle tends to 0 while the mesh size of partition does not tend to zero as the limit approaches infinity of sequence of partitions.