[mjw]

In case the measure theory put anyone off: you don't need Dirichlet Processes for plain LDA, just the finite-dimensional http://en.wikipedia.org/wiki/Dirichlet_distribution (which isn't so bad and a very useful tool in Bayesian stats as the conjugate prior for discrete observations)

For some of the non-parametric variants like hierarchical dirichlet process LDA, you need DPs, but that stuff is pretty hardcore -- don't walk before you can run.

Another route to LDA (assumes some Bayesian stats basics):

* Learn a bit about Markov chains if you don't know them already * Read up on sampling-based approximate inference methods and find a proof that a Gibbs sampler converges (or just take it on trust...) * Read the classic Griffiths and Steyvers paper deriving a collapsed Gibbs sampler for LDA [1]

[1] http://www.pnas.org/content/101/suppl.1/5228.full.pdf