When does basic integral theory that you learn in a first year real analysis course lead to measure theory What techniques.. do I need to make the transition less painful Measure theory seems much more abstract.
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It doesn't really, at least not in a natural way. Perhaps a less abstract approach would be to consider measure theory from a probability perspective, how to define events in a manner that is consistent. – copper.hat May 28 '19 at 16:45
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1Not sure what is painful about measure theory. It seems like a relatively straightforward generalization of interval lengths and areas bounded by curves. The next good example to consider, I suppose, is the example of center of mass of a rod with nonconstant density. – rschwieb May 28 '19 at 16:48