Oct 9, 2017
Here is the complete current notes. Everything up to Section 12.7 are correct, which you can cite. I did have some shuffling of propositions around due to new insight gained in the study. I am thinking about whether to impose the condition that an integral is said to exist if it is absolutely integrable. This is in line with the definition of σ-finite banach space valued measures. If the total variation is unbounded, then the measure is not defined. In the current version, an integral may exist even though it is not absolutely integrable. But, then, none of the usual operations that we took for granted for an integral is guaranteed to be valid. So, I am thinking about this change, which is a major rework of Chapters 11 and 12.