Day 6 - An Assortment of Dishwater

Another lonely day at home, just me and the dog. Julia was gallavanting in Leicester, and the rest of my family was out at work, leaving my itinerant student self to roam the echoing halls like an industrious ghost.

Industrious, indeed! I did some housework, played with the dog, tidied the kitchen, read some of Rudin's analysis, and watched SIX episodes of Frasier. My stamina astounds me. I also watched the Dark Knight whilst attempting to construct the rest of my Ork Horde.

Unfortunately, the glue is either too weak, too old, or inproperly applied, so most of my good work so far probably won't last too long. Such is a summary of the day's events, but that's not what you came for, is it? You want me to dish the dirt, the skinny, the low-down, the real Red Mary on measure theory.

You sly dog, you. Wassamatter, Riemann integral not good enough for you anymore? Integrating continuous functions over compact intervals just doesn't get your jazz flowing? Don't worry, you crafty mathematical artiste. Lebesgue integration can sort out your troubles.

Even more so, the definition can be extended to work out an integral for ANY measurable function on ANY measure space, not just the same boring old real numbers.
In fact, by defining different measures on the same space, lots of different facts from different areas turn out to be special cases of quite broad theorems in measure theory.
For example, an infinite sum is 'really' just a normal integral with counting measure rather than Lebesgue measure.
Don't understand what I'm talking about? Check Wikipedia for now. When I figure out how to put nice Latex into blog posts, I might start doing some nice exposition.

Well, I've just received an interesting proposition: Blood Bowl against an old opponent. He mocks me with his "\o/" smiley. So you can raise your arms above your head, eh? He's just trying to make me jealous. I've had the nickname "Acute armpit" since Year 4. Sickening.

Today's trivia: "Do not accept a bribe, for a bribe blinds those who see and twists the words of the righteous." Thanks, Exodus 23:8!