Systems and electrical engineering graduate students often take a course on stochastic systems (a.k.a. "Probabilistic Systems Analysis"). A typical course will present such topics as multivariable probability distributions, auto- and cross-correlations (and Fourier transformations of them), Ergodicity, stationarity, etc.
Students wanting a more advanced treatment after completing the above often gravitate towards a more rigorous Stochastic Processes course in the math department, which normally smacks them over the head with the concept of Measure Theory, which throws them for a loop, even if some have taken a course in advanced engineering mathematics.
What is the best way to bridge the gap between what is a more applied treatment of these probabilistic concepts into the more abstract notions, particularly for students that may not have had a graduate-level Real Analysis course?