maths.free › Measure Theory
Measure Theory
Lebesgue measure and integral, σ-algebras, convergence theorems.
Сургамж
integrate 1/10 dx from 2 to 5
Advanced
The Lebesgue integral and convergence theorems
Integrating by slicing the range instead of the domain; monotone and dominated convergence.
integrate e^(-x) dx from 0 to oo
The Riemann integral breaks on functions that jump too much. Measure theory rebuilds integration from "size of a set" upward, and the Lebesgue integral that results is the one probability theory and analysis actually use.
Сургамж
Measuring sets
The integral
Зарим хичээлүүд нь нээлттэй текстээс авсан: Wikipedia. Сургалтын хуудас бүрийн эх үүсвэр, лицензийг тодорхойлно.
Энд ашигласан тэмдэгтүүд
Бүх тодорхойлолт, зураг, үсгийн утгыг харахын тулд ямар ч тэмдэгтийг дарна уу.
Хүмүүс асуудаг асуултууд
What is wrong with the Riemann integral?
It fails on functions that oscillate too much, and it does not interact well with limits: the limit of integrable functions need not be integrable. Lebesgue's integral fixes both.
Тоглоомын хуудаснаа бичээд эсвэл зур. Бүх алхам, зураг, хариулт нь асуулт асуух хүртэл нуугдаж байдаг. Засварлах →
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