Concerning Uncountable Sums

Sums are a beautiful notion which are sometimes taken for granted. 2 + 2 = 4, the sum from 1 to infinity of 1/2n is equal to 1, and so forth. In the case of countably infinite sums, questions of convergence become important. But what happens when you have a sum over uncountably many summands? It . . . [Read More]