This is (or was) a common procedure in molecular biology. You would culture microbes in a sealed container, that contained a lit candle. As the candle burned out, it exhausted most of the oxygen in the system, suitable for growing microaerophiles, in your case, you're fermenting yeast, but this procedure is used also for human pathogens. It's a pretty big surprise, for many people, that the interior of the human body has very little free oxygen, our cells snap it up too efficiently.
Yeast are facultative, if they have oxygen, they'll consume nutrients and grow in size and reproduce. Without oxygen, their enzymes simply consume glucose to ethanol and CO2 -- you're probably going to measure one of these products, and it'll be easier to quantify, if not muddied by the myriad of products produced by aerobic growth.