Yes, I'll edit in those synonyms for reference. In defense of "Informativity" and "inf", they're defined for a single event in section 2.3 of this paper:

http://www.springerlink.com/content/m628x0774718237k/

"Information value" is Shannon's term. I just picked the terms I liked best :)

Nice application to the tennis balls problem! I'd heard that a long time ago, but hadn't though about it since I met information theory.