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Measure Theory
Lebesgue measure and integral, σ-algebras, convergence theorems.
មេរៀន
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.
មេរៀនបន្ថែម
Measuring sets
The integral
មេរៀនមួយចំនួននេះត្រូវបានកែប្រែពីអត្ថបទបើកចំហ ៖ Wikipedia. ទំព័រមេរៀននីមួយៗមានឈ្មោះប្រភព និងអាជ្ញាបណ្ណរបស់វា ។
និមិត្តសញ្ញាដែលបានប្រើនៅទីនេះ
ចុចនិមិត្តសញ្ញាណាមួយសម្រាប់ការកំណត់ពេញលេញ រូបភាព និងតួអក្សរនីមួយៗមានន័យអ្វី ។
សំណួរដែលមនុស្សសួរ
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.
វាយវា ឬគូរវានៅលើទំព័រកម្មវិធីដោះស្រាយ ៖ ជំហាននីមួយៗ រូបភាព ចម្លើយដែលលាក់រហូតដល់អ្នកសួរ ។ ដោះស្រាយ →
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