I am looking for a signal processing textbook that uses real, complex, and functional analysis with measure theory. In other words, mathematically rigorous signal processing. Specifically, I prefer the kind that takes time to review all the topics from mathematical analysis before jumping into the fire (due to a potential experience deficit in some analysis topics), but will gladly consider any rigorous signal processing. A Mathematical introduction to signal and systems by A. D. Lewis is pretty much what I am looking for, however, only first volume is available, so I need an equivalent. Please inform me of any textbooks that you know of that fit my search criteria, and I shall be grateful in return. Thank you for your time.