Dominated convergence theorem

Imagine you have a bunch of cookies, and you want to figure out how much sugar is in all of them put together. Now, some of the cookies might have more sugar than others, but you can still figure out the total amount of sugar by looking at the biggest cookie. Let's call this the "boss cookie".

The dominated convergence theorem works kind of like that. It helps us figure out the total amount of something called the "integral" by looking at a boss function. This boss function is called the "dominating function".

Let's say you have a bunch of little functions that you're trying to add up, just like the cookies. Each of these little functions might be a little different, but they're all going to be less than or equal to the dominating function. This dominating function is like the boss cookie - it's the biggest and strongest one.

The dominated convergence theorem tells you that if you have a bunch of little functions that are all smaller than the dominating function, and the dominating function is something you can integrate, then you can add up all the little functions and get the same answer as if you just integrated the dominating function by itself.

So, just like you can find out how much sugar is in all the cookies by looking at the boss cookie, you can find out the total amount of something called the "integral" by looking at the boss function, called the dominating function.