We will first follow Pugh's approach, then we will cover Tao's approach in exercises.
Use undergraph of a non-negative function to define measurability and its measure. If the measure is finite, then call this function integrable.
Monotone convergence theorem. (Recall upward/downward continuity theorem)
Completed undergraph (not the closure of the undergraph, but just fiberwise closure). Can be used interchangeably with the undergraph
upper and lower envelope sequence of a function, just like how one define the liminf and limsup.
Dominated Convergence theorem.
Many examples: running bump, shrinking bumps.
math105-s22/notes/lecture_7.txt · Last modified: 2022/02/08 21:41 by pzhou