The 21 April Day Thread Talks about Measure Theory

OK fine, not really, just the barest of basics before everyone’s brains oozes out of their skull through pure confusion (including me)

A measure is a function that assigns a non-negative real number or +∞ to (certain) subsets of a set X. 1

A measure must further be countably additive: if a ‘large’ subset can be decomposed into a finite (or countably infinite [a cardinality that is the same as that of the integers]) number of ‘smaller’ disjoint subsets that are measurable, then the ‘large’ subset is measurable, and its measure is the sum (possibly infinite) of the measures of the “smaller” subsets.

From this baseline, we can generalizes the intuitive notions of length, area, and volume: mass distributions with meaningful distributions that can account for ‘paradoxes’ like the Banach-Tarski paradox 2

Got all that? No? Ah well whatever, enjoy an Go! Team video for your efforts/troubles in reading (or trying to read) all that nonetheless: