Answer: I need a little more information to diagnose your problem, but I'm going to give you two possibilities and an excellent source in Tucson that will be able to identify what's on your cabbage.
There's a white powdery fly called a whitefly (clever name, huh?), but it usually shows up in late summer when temperatures are higher. (Whiteflies thrive in the cotton fields and when growers denude the plants, whiteflies head in droves to the nearest landscapes.) Whiteflies usually aren't a big problem with cool-season crops like cabbage.
There's also a fungal disease that looks like a white powder called powdery mildew. It spreads quickly when the humidity is high and temperatures are between 50F and 90F.
I can't really suggest a solution without knowing what you have. If you contact the University of Arizona Cooperative Extension office in Pima County and ask for the Master Gardener desk, they will be able to assist you further. You can also take a sample of the bug and affected plant to their office. Good luck!
University of Arizona Cooperative Extension
4210 N. Campbell
Tucson, AZ 85719
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