Clopen-Analysis/latex - Open Analysis Project
Clopen Analysis is an online compendium about real analysis, specializing in measure theory. The material is at the level of a graduate-level course in real analysis.
The main novelty of Clopen Analysis is that it is freely available, and written by volunteers on the internet, possibly including you. In fact, any reader can contribute content to Clopen Analysis via GitHub, and Clopen Analysis is dependent on the contributions of its readers. Decisions about the content of Clopen Analysis shall be made by clear community consensus, or a majority vote if consensus is unclear. At least for the present, Aidan Backus manages the project, but this is subject to change.
Clopen Analysis was originally based on, and certainly would not exist, without the lecture notes of Rieffel \cite{Rieffel1970}, which were novel at the time for their treatment of integration valued in Banach spaces from the getgo. However, the proofs that appear in Clopen Analysis are drawn from a variety of sources, including but not limited to the books of Lang \cite{lang2012real}, Pugh \cite{pugh2013real}, and Rudin \cite{rudin1978real}.
The added level of abstraction caused by the fact that integrals are Banach-spaced valued does not meaningfully increase the difficulty of proofs, with the exception of the characterization of measurable functions as those for which preimages of Borel sets are measurable. In spite of the level of abstraction, we have strived to include many examples, and to keep the content at a level that anyone with an undergraduate education in mathematics, including but not limited to real analysis at the level of Pugh \cite{pugh2013real}, can peruse Clopen Analysis.
Contributing
If you want to contribute TeX code for theorems, definitions, problems etc. please feel free to send over a PR!
If you want to contribute to any of the build system, automation, or other pieces (or if you just aren't sure if you should submit a PR) you can start a discussion to figure out whats best.
There is a Gitter for organization members, but we also have a public-facing Discord server for discussion.
Lastly if you find an immediate issue, e.g. an error in any of the math, please file an issue!