I really don't know much about this kind of thing, but having read some of the responses, is it fair to say that you don't understand how bacteria respire aerobically without mitochondria? Well the mesosomes will be similar to the cristae of mitochondria (to increase surface area for ox phos) and the thing to remember here is that mitochondria derive from bacteria, so bacteria are essentially free-living mitochondria and therefore they will be able to do aerobic respiration in an identical way to eukaryotic cells. So yh, if mesosomes do have a purpose then one would assume it's to increase the surface area for enzymes involved in aerobic respiration. I have just answered that based on other responses in the thread, I've never heard of mesosomes before ngl