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Course prerequisites

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I am starting to register for courses (Doing stats MA, planning on applying for PhD if I consider I can handle it at that time). Could anyone here tell me about this:

Is a course in integration theory and a self-exploration of Baby Rudin considered proper prerequisites of measure-based probability theory?

(The course material is somewhat equivalent to Royden's real analysis Part I, but is taught easier. I read Chapter 1-6 of Rudin and finished nearly all the exercises. I also read C7 but found problems extremely difficult. Of course I know C11 due to the course I've taken but not familiar with the rest)


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