I'm in a similar position as well - perhaps at just a wee bit higher level (am learning grad-level math by myself). Below is a list of books that I have enjoyed. Some might perhaps be at a slightly higher level than you…
I'd agree with your assessment of Royden. Another fantastic book on Lebesgue Integration/Measure theory is Lebesgue Integration in Euclidean Spaces by Frank Jones. Fantastic textbook.
I'm in a similar position as well - perhaps at just a wee bit higher level (am learning grad-level math by myself). Below is a list of books that I have enjoyed. Some might perhaps be at a slightly higher level than you…
I'd agree with your assessment of Royden. Another fantastic book on Lebesgue Integration/Measure theory is Lebesgue Integration in Euclidean Spaces by Frank Jones. Fantastic textbook.