I'm reading about the Glivenko-Cantelli theorem and at first blush, it reminds me a lot of Riemann Sums, discrete math, and maybe even the fundamental theorem of calculus in general. The formal statement of the theorem for both the Condtinuous Distribution and general forms seems kind of obvious to me given other theorems in mathematics, so I was surprised to learn that it was formalized in the 20th century.

Does anyone know why it took so long to state (not prove) the Glivenko-Cantelli theorem? Was it because of some late breaking mathematical discovery, or was it a product of the state of statistical analysis at the time relative to other mathematical fields? Or was Glivenko-Cantelli a revolutionary observation and I'm not really getting it?


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