still studying...

me: (on the phone, leaving a voicemail for ben) ben! i have an analysis emergency of epic proportions... eric and me are irate that we don't understand why the dirichlet function restricted to the unit interval isn't a counterexample to lusin's theorem... it's the characteristic function of a measurable set, so it freakin well better me a measurable function... but it's discontinuous everywhere so how the heck do you find a compact set with measure arbitrarily close to 1 where it's continuous... find me an answer or i'm gonna cry that math is fundamentally screwed up and i'll find something new to do with my life... catch you later"
me: (to eric) see wasn't that a good message?
eric: yes, it was hilarious, but i have TWO words for you
me: what's that
eric: drama queen

cantor sets (see here) may be all pretty and cool at a first glance, but when studying for a qual, really screw up the world..

it really makes me unhappy that by lusin's theorem, the Dirichlet function, which is discontinuous EVERYWHERE has a compact set in the unit interval with measure almost as big as the unit interval that it's continuous on. (note, the set is a "fat cantor set", like in the initial link... it also makes me angry that there are compact sets of positive measure that don't contain any intervals.)

math can be soooo twisted.... down with set theory altogether now!