# Multidimensional Integration

Here, you find my whole video series about Multidimensional Integration in the correct order and I also help you with some text around the videos. We will need some knownledge from the Multivariable Calculus course and the Measure Theory course. If you have any questions, you can contact me and ask anything. However, without further ado let’s start:

#### Part 1 - Lebesgue Measure and Lebesgue Integral

Let’s start the video series by stating the definition of the important Lebesgue measure. To understand the whole construction, you have to watch my Measure Theory course. However, even if you didn’t watch it, you should grasp the essential properties this measure has. The conclusion in the end is that we have a much more powerful integral on the real number line. This one generalizes the Riemann integral, you might know from Real Analysis.

#### Part 2 - The n-dimensional Lebesgue Measure

In the second part, the power of the general Lebesgue integral comes really through. It’s no problem at all to generalize everything quickly to higher dimensions. This is something where the Riemann integral really struggles with, but with the Lebesgue integral, everything is simple and fast.