Alternative approaches to probability theory I'm undergraduate student in probability theory (and its applications). There are lots of different and definitely good text on standard, functional analysis-based approach, but I'm interested in alternative approaches - maybe, some more algebraic variants. Could you name some ideas/papers/texts about this? I'm especially interested in the ones those can be used in applied problems (such as financial mathematics or something). I've surely saw some approaches in Wikipedia, but I have absolutely no idea of using them in practical problems.
 A: Peter Whittle's "Probability via expectation" is a very nice book. In taking expectation (rather than probability measure) as a starting point, the text manages to


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*Avoid measure theory almost entirely

*Get to interesting applied problems very quickly 


Though Whittle (probably deliberately) never says this, the approach here is essentially the `Daniell integral' approach to integration theory, cast in a probabilistic context. The text is (in my opinion) spectacularly well written, both in terms of the choice/order of material, and in the quality and warmth of the written English. I cannot think of many books of this type (i.e. one advocating an 'alternative' approach to the development an established theory) which cover so much material quite so masterfully whilst remaining so focused and true to their founding premise.
A: Yuri,  you may have a look at the introductory probability book by Henk Tijms, Understanding Probability. An excellent book having the nice feature that simulation is used throughout to develop probabilistic intuition.
