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Initially, there was an ambitious plan to write a comprehensive book on quantitative finance with readable and thorough introduction to necessary advanced mathematics. It turned out to be a little bit too much ambitions. So I decided to limit myself to the [one of the] most important part: to write a user-friendly introduction to the Lebesgue measure theory. Currently, there are many good books on financial mathematics but I do not know any book on measure theory, which I would recommend for a self-study. S