Measure Theory 3 | What is a measure? [dark version]

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🌙 There is also a dark mode version of this video:    • Measure Theory 3 | What is a measure? [dar...  
🔆 There is also a bright mode version of this video:    • Measure Theory 3 | What is a measure?  

🔆 To find the YouTube-Playlist, click here for the bright version:    • Measure Theory  
🌙 And click here for the dark version of the playlist:    • Measure Theory [dark version]  

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We discuss sigma algebra, measures, and integration. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: https://tbsom.de/s/community

This is part 3 of 22 videos.

00:00 Introduction
00:26 Measure - Definition
03:08 Empty set has measure zero
03:35 Additivity
05:59 Sigma-additivity
07:54 Summary
08:43 Measure space
09:18 Examples
09:40 Counting measure
12:30 Dirac measure
14:12 Lebesgue measure

#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
#Probability

I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

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