Lebesgue measure is a lot of annoying terminology, but the end result are basically integrals that work like how you intuitively "want" them to work. Basically

Lebesgue measure is a lot of annoying terminology, but the end result are basically integrals that work like how you intuitively "want" them to work. Basically so long as you never have to evaluate one using the actual definition then you're gucci, just pretend like you're a physicist and think about it terms of things like point-masses.