What would be an easily accessible book dealing with Bochner integration as applied to probability theory (I'm looking to understand random elements and their basic related concepts in a formal yet vaguely conceptual manner).
Preferably, I'm looking for a book that develops everything from scratch (so that i don't miss out on any important conceptual points).
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2$\begingroup$ I don't know about "vaguely conceptual", but Diestel and Uhl's book Vector Measures gives a very thorough approach to the basics. $\endgroup$– Yemon ChoiCommented Oct 8, 2014 at 21:25
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$\begingroup$ Have you seen Bochner integration at all and just want to see applications of it in probability theory, or are you asking for a source where you can learn about it with probability theory as the motivating topic? $\endgroup$– KConradCommented Oct 9, 2014 at 2:24
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1$\begingroup$ The second one mostly $\endgroup$– ABIMCommented Oct 9, 2014 at 2:54
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1$\begingroup$ Hytönen, T. et. al. (2016) Analysis in Banach Spaces is a good reference. Its subtitle goes Volume I: Martingales and Littlewood-Paley Theory. $\endgroup$– Hirofumi ShibaCommented Jun 26, 2023 at 8:05
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