Being a junior(3rd.year) undergraduate in mathematics, I would like to learn how serious papers of mathematics do the proofs rigorously as opposed to textbooks and proffessors in lectures and I wish to see this by myself. For this reason , I just want to read at least one paper which I can understand the topic and proofs.
Though the aim of this reading process is to learn the extent of rigorousness in papers , I want also the subject to interest me so that I would learn something. That is why I might choose the topics somewhat related to real analysis since I consider doing Phd on real& functional analysis or probability & stochastic analysis.Hence, subjects could be Real Analysis, Game Theory, Probability or Stochastic Processes.
The thing is that I should be able to understand the paper to avoid throwing the paper away. I am at the level of Apostol's Mathematical Analysis(Point set topology ,metric spaces, differentiation &integration, continuity, uniform convergence, series and sequences of functions etc.) and I took a course on Lebesgue Integration which started Lebesgue Theory by sequence of step functions. I have not taken or read any thing on Stochastic Calculus but I know Applied Probability and Statistics at the level ,say undergraduate engineering student.
With all these in mind, which spesific paper do you suggest me to read?
EDIT based on comments:
1) The paper that I am looking for can be any theorem which is usually a subject of an undergraduate real analysis courses or from a textbook on real analysis. To give some examples, Fubini's Theorem, Beppo-Levi's Theorem in Lebesgue Integration or Banach's Fixed Point Theorem, Arzela-Ascoli Theorem, Baire Theorem etc. on Analysis can be candidates .
Best Answer
Another Suggestion:
A simple proof that $\pi$ is irrational
It is a one page proof. It is not a proof of a major theorem, and questionably fits into your field though.