Absolute continuity (measure theory)
Absolute continuity is like when a grown-up tells you to always eat your vegetables before you can have dessert. They are making sure that you only get the good stuff after you have done something good first.
In math, absolute continuity is when one type of measure (let's call it the grown-up) only lets another type of measure (let's call it the dessert) happen if certain conditions are met.
For example, if you have a line and you want to measure the length of a piece of it, absolute continuity means you have to use a certain type of measure called Lebesgue measure. If you don't use Lebesgue measure, then you can't get the dessert of knowing how long the line is.
In other words, absolute continuity is a way of making sure that the measurements we get are good and accurate, just like eating vegetables is good for our health.
In math, absolute continuity is when one type of measure (let's call it the grown-up) only lets another type of measure (let's call it the dessert) happen if certain conditions are met.
For example, if you have a line and you want to measure the length of a piece of it, absolute continuity means you have to use a certain type of measure called Lebesgue measure. If you don't use Lebesgue measure, then you can't get the dessert of knowing how long the line is.
In other words, absolute continuity is a way of making sure that the measurements we get are good and accurate, just like eating vegetables is good for our health.