Finitely additive measure

Imagine you have a bunch of toys, and you want to count them to see how many you have. You start counting and realize that you have six toys.

Now, let's pretend that you have a special power that lets you measure things in a different way. Instead of just counting how many toys you have, you can also measure how heavy they are or how tall they are.

Let's say you decide to measure how heavy your toys are. You take out a scale and weigh each toy to see how heavy it is. Now you know not only how many toys you have, but also how heavy they are.

But here's the thing: your special measuring power only works on one toy at a time. You can't put all the toys on the scale at once and get a total weight. You have to weigh each toy separately and then add up all the weights to get the total weight of all your toys.

This is kind of like a finitely additive measure. A measure is a way of determining the size of something. In this case, we're measuring the "size" of our set of toys. Finitely additive means that we can only add up a finite (limited) number of things at a time. We can't add up an infinite number of things, like all the toys in the world.

So a finitely additive measure is a way of figuring out the "size" of something by adding up the size of each individual part, as long as we're only adding up a limited number of parts.