In this chapter, we treat the general theory of the measure of lines, areas, volumes, and sets in even higher dimensional spaces. The theory is guided by elementary geometrical facts. In particular, we will assign the length measure to intervals, the area measure (length times width) to rectangles, and the volume measure (length times width times height) to rectangular boxes.
KeywordsTopological Space Lebesgue Measure Measure Space Measure Theory Outer Measure
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