Feller was an ebullient man, who would rather be wrong than undecided.
Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.
The author discusses valueless measures in pointless spaces.
The library is the mathematician's laboratory.
The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method.
Mathematics - this may surprise or shock some - is never deductive in creation.