Measure theory: the heart of the matter (Q1088801)

This is an excellent exposition of the evolution of geometric measure theory from Euclid to Lebesgue. The ''heart of the matter'' referred to in the title is what the author calls the ''paving stone technique'' - the idea of measuring complicated or irregular areas by exhausting or covering them with simple areas whose measurements are known. The author describes and explains very clearly the different ways in which the paving stone technique has been used in Euclid's ''Elements of Geometry'' and later on to extend classes of measurable areas and of integrable functions until geometric measure theory reached its maturity with Lebesgue's construction of measure and integral. The author also emphasizes the role of the paving stone idea in probability theory, and he briefly discusses the importance of abstract measure theory developed after Lebesgue in the foundations of probability theory and mathematical statistics.