I know some undergraduate analysis books (like Baby Rudin) has its last chapter about Lebesgue theory but that book already is called "Principles of Mathematical Analysis" so the book wouldn't be used for a calculus course.
I'm looking for a book that (1) is about calculus but (2) directly references analysis topics and what kind of courses come after calculus classes.
Most often the books give a vague idea of "this topic will be seen in more advanced/future/later courses" but there's nothing explicitly mentioned.
Best Answer
Gerald Folland's Advanced Calculus I used for the Indiana University Analysis Tier 1 qualifying Exam, which expected you to know calculus topics from an analytic perspective. It does exactly what you want in terms of being "about calculus" but directly referencing analysis topics.
Ch. 1 is where it references the analysis topics, and in Ch. 4 there is a brief section on Lebesgue Measure and Lebesgue Integrals, and it also talks about "rectifiable sets" in multiple dimensions.