Weakly measurable function

A weakly measurable function is like a magic trick where you can see some things, but not everything. Imagine you are playing hide-and-seek with your friend. You can see where your friend is hiding if they are right in front of you, but if they are hiding behind a tree, you can't see them. A weakly measurable function is like the friend hiding behind the tree, you can't see it directly, but you can find it indirectly.

In math, we have something called a measure which tells us how much of something there is. For example, if we have a box of chocolates, we can measure how much chocolate is in it by counting the number of chocolates inside. But sometimes we can't count everything, for example, if we have a bowl of water, we can't count the number of water molecules in it. In this case, we use something called a weak measure that tells us approximately how much water there is in the bowl.

Similarly, a weakly measurable function is like a bowl of water, we can't measure it directly but we can measure it indirectly. We can do this by looking at how the function interacts with other functions that we can measure. For example, we can see how the function behaves when we multiply it with another function or integrate it over certain intervals. From these interactions, we can tell approximately how much of the function there is, even though we can't see it directly.

So, in summary, a weakly measurable function is like a hidden friend behind the tree or a bowl of water that we can't see directly, but we can find indirectly by looking at how it interacts with other things we can measure.