Fatou–Lebesgue theorem
The Fatou-Lebesgue theorem is like trying to count all the candies you have in a big jar. Imagine you have a really big jar (this is called a set) of candies and you want to count how many candies are in it. However, you can only take out one candy at a time because your hand is too small to grab them all at once.
First, imagine you take out one candy at a time and you know the total number of candies. This is called the Lebesgue theorem. It says that the total number of candies in the jar is the addition of all the candies, one by one.
Now, let's imagine you start to take out candies but you don't know the total amount of candies in the jar. Instead, you start to group the candies based on their colors or flavors. The Fatou theorem says that if you add up the number of candies in each group, it will always be less than or equal to the total number of candies in the jar.
So, in summary, the Fatou-Lebesgue theorem helps us count the total amount of candies in a jar by either adding them one by one or grouping them and adding the groups together. And it always gives us the correct answer.
First, imagine you take out one candy at a time and you know the total number of candies. This is called the Lebesgue theorem. It says that the total number of candies in the jar is the addition of all the candies, one by one.
Now, let's imagine you start to take out candies but you don't know the total amount of candies in the jar. Instead, you start to group the candies based on their colors or flavors. The Fatou theorem says that if you add up the number of candies in each group, it will always be less than or equal to the total number of candies in the jar.
So, in summary, the Fatou-Lebesgue theorem helps us count the total amount of candies in a jar by either adding them one by one or grouping them and adding the groups together. And it always gives us the correct answer.