# The Problems with Measures

## Introduction

So we’re trying to abstract the notion of “mass” to shapes whose geometry isn’t easily understood.

We start by definining a notion of distance. Okay, that’s a topology.

Because if you can define distance between points, if points are sufficiently far apart, then you can talk about space.

Space necessitates that things are not the same. Things, objects, collections. Sets. Functions. I’m getting ahead of myself.

If you can talk about space bewteen points (distance) then, you can talk about things between spaces between points.

But between you and me, something amazing happened…

Now we’re all taking up space.

## Tonelli’s Theorems, Limits and Colimits

~~Tonelli’s theorem says that the morphism mu commutes with colimits (cartesian product of measure spaces).~~