Sigma-additive set function
Okay kiddo, let's talk about sigma-additive set function.
Imagine you have a big bag of candy, and you want to divide it into smaller bags for your friends. A sigma-additive set function is like a special way of dividing up the candy that has some rules to follow.
First, the function is called a "set function" because it deals with sets of things, like piles of candy. The function has to follow certain rules:
1) If you have two sets of candy and they don't overlap (none of the same candies are in both sets), you should be able to add up the amount of candy in each set to get the total amount of candy.
2) If you have more than two sets of candy, and they don't overlap, you should be able to add up the amount of candy in each set to get the total amount of candy.
3) If you have an infinite number of sets of candy, and they don't overlap, you should still be able to add up the amount of candy in each set to get the total amount of candy.
So a sigma-additive set function is a special way of dividing up your candy into sets that follows these three rules. It's like a math wizard who can always figure out exactly how much candy you have, no matter how you divide it up.
Imagine you have a big bag of candy, and you want to divide it into smaller bags for your friends. A sigma-additive set function is like a special way of dividing up the candy that has some rules to follow.
First, the function is called a "set function" because it deals with sets of things, like piles of candy. The function has to follow certain rules:
1) If you have two sets of candy and they don't overlap (none of the same candies are in both sets), you should be able to add up the amount of candy in each set to get the total amount of candy.
2) If you have more than two sets of candy, and they don't overlap, you should be able to add up the amount of candy in each set to get the total amount of candy.
3) If you have an infinite number of sets of candy, and they don't overlap, you should still be able to add up the amount of candy in each set to get the total amount of candy.
So a sigma-additive set function is a special way of dividing up your candy into sets that follows these three rules. It's like a math wizard who can always figure out exactly how much candy you have, no matter how you divide it up.
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