The LEBESGUE Integral: The Most Powerful and Brilliant of All! - YouSciences by GIUX - World Latest Movie, Series, Videos and Trailers | fetery.com

The LEBESGUE Integral: The Most Powerful and Brilliant of All!

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YouSciences by GIUX

Published on Nov 12, 2024

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⭐️Subscribe and get on the science spaceship ⭐️: / @yousciences The first time we encounter the concept of integral we are taught a procedure for dividing a domain of a function into many small pieces whose sum gives us the area under the graph! You might apparently imagine that only this type of integral exists, the Riemann one. But that is not the case! The most powerful of all is the Lebesgue Integral! Which solves the problem of integration even for strange functions like the Dirichlet one and other similar devilries. In this video we will start from the beginning, from the rudiments of Riemann integration and we will discover how from this we move on to a new ingenious integration procedure, the Lebesgue one, we will talk about the measure theory of Borel sigma algebras and null measures; all concepts that are the foundation of advanced sectors of engineering and physics such as quantum mechanics, signal theory, integral transforms etc. #lebesgue #integration #riemann #mathematics #physics #doctorgiux #giux #yousciences #science #maths #geometry ⭐️SUPPORT THE PROJECT⭐️: https://www.paypal.com/donate/?hosted... ????Our Subscribers????: https://www.yousciences.it/membership/ Where to find me ????: ➤YOUSCIENCES: https://www.yousciences.it/ ➤OFFICIAL WEB SITE: https://www.giuseppesottile.it/ ➤INSTAGRAM: @yousciences @___giux___ ➤FACEBOOK: / giuseppe.sottile.56 ➤LINKEDIN: / giuseppe-sottile-3a8599b0 ➤TELEGRAM: https://t.me/joinchat/abNZYJqE7MVlODA0 ➤TIKTOK: https://www.tiktok.com/@yousciences?l... Other Various videos ⚛️: • Various Insights: https://it.wikipedia.org/wiki/Integra... https://it.wikipedia.org/wiki/Misura_... https://it.wikipedia.org/wiki/Sigma-a... ????️ VIDEO STREAM ALL: https://www.yousciences.it/videostream/ https://www.giuseppesottile.it/video.php Chapter summary 00:00 Ouverture 01:09 Riemann integration 03:49 Anomalies of the Riemann integral 08:40 Continuity 10:37 Function of Dirichlet 12:40 Limit under the integral sign 14:25 Lebesgue's Idea 15:35 The bit and pieces 18:17 The Monster 20:50 Measure Theory 23:40 Characteristic Functions 26:10 Step Functions 27:49 The Lebesgue Integral 33:10 Resolution of the Dirichlet Function (Zero Measure) Executive Production by Giux

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