Timeline for Defining the integral of a function using the product measure
Current License: CC BY-SA 3.0
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| Aug 31, 2012 at 6:34 | comment | added | Jochen Wengenroth | Yes, it is not obvious that the iterated integral is well defined. But this is a technical problem which (for $\sigma$-finite measures) can be solved e.g. using Dynkin systems and, as you said, the monotone convergence theorem. However, imagine an average student in a course on probability theory: He could disregard all existence and measurability problems and nevertheless understand the proofs of almost all important results including the construction of product measures. | |
| Aug 30, 2012 at 17:06 | history | answered | Nik Weaver | CC BY-SA 3.0 |