A short proof of the Doob-Meyer theorem. Beiglböck, M., Schachermayer, W., & Veliyev, B. Stochastic Process. Appl., 122(4):1204–1209, 2012.
A short proof of the Doob-Meyer theorem [link]Paper  doi  bibtex   
@article{MR2914749,
	Author = {Beiglb{\"o}ck, Mathias and Schachermayer, Walter and Veliyev, Bezirgen},
	Coden = {STOPB7},
	Date-Added = {2012-09-24 10:50:25 -0500},
	Date-Modified = {2012-09-24 10:56:03 -0500},
	Doi = {10.1016/j.spa.2011.12.001},
	Fjournal = {Stochastic Processes and their Applications},
	Issn = {0304-4149},
	Journal = {Stochastic Process. Appl.},
	Mrclass = {60G05 (60G07 60G44)},
	Mrnumber = {2914749},
	Number = {4},
	Pages = {1204--1209},
	Title = {A short proof of the {D}oob-{M}eyer theorem},
	Url = {http://dx.doi.org/10.1016/j.spa.2011.12.001},
	Volume = {122},
	Year = {2012},
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	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.spa.2011.12.001}}

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