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Measure Theory

  Measure theory, in mathematics, began as the response to one specific question. Suppose you were given a boundary in space. What is the particular surface which has this boundary and which has the smallest possible area? (The question is usually generalized to higher dimensions.) In three dimensions, the surface is that which would be taken up by a soap bubble given the boundary as a frame. This question is essentially one of topology, but from the work in measure theory applications have been found in many branches of mathematics, as well as in cosmology. Measure theory has also provided the basis for modern views of the integral calculus. SMcL  



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