Lebesgue–Stieltjes integration
Lebesgue–Stieltjes integration is a fancy math way to add up numbers. It's like when you count how many candies you have, but using a more complicated method.
First, imagine you have a line, and on this line, you put little marks at certain points that represent values or numbers. Let's say these marks show how much money you have, with different marks representing different amounts of money.
Next, someone tells you to add up all the money you have based on these marks, but you can't just count the number of marks and multiply them by a certain amount, because some marks might be farther apart than others.
To solve this problem, you can divide the line into little parts and measure the distance between the marks and add them all up. But instead of just adding them up, you also want to take into account the value of each mark.
That's where the fancy math comes in. You create a new kind of function, called the Stieltjes function, which represents the distance between the marks. Then you use another special function, called the Lebesgue integral, to help you add up all the different values of the marks, taking into account the distances between them.
Using these two functions together, you can add up all the values of the marks on the line to calculate the total amount of money you have, and this is called Lebesgue–Stieltjes integration.
First, imagine you have a line, and on this line, you put little marks at certain points that represent values or numbers. Let's say these marks show how much money you have, with different marks representing different amounts of money.
Next, someone tells you to add up all the money you have based on these marks, but you can't just count the number of marks and multiply them by a certain amount, because some marks might be farther apart than others.
To solve this problem, you can divide the line into little parts and measure the distance between the marks and add them all up. But instead of just adding them up, you also want to take into account the value of each mark.
That's where the fancy math comes in. You create a new kind of function, called the Stieltjes function, which represents the distance between the marks. Then you use another special function, called the Lebesgue integral, to help you add up all the different values of the marks, taking into account the distances between them.
Using these two functions together, you can add up all the values of the marks on the line to calculate the total amount of money you have, and this is called Lebesgue–Stieltjes integration.