Unit · year 3
MU-302 · Measure & Integration
Threads space · chance5 theorems
The Lebesgue theory: a robust notion of size and integral.
Theorems in this unit
T-084
Carathéodory's extension theorem
A premeasure extends to a genuine measure.
T-085
The monotone convergence theorem
Integrals commute with increasing limits of non-negative functions.
T-086
Fatou's lemma
The integral of a liminf is at most the liminf of integrals.
T-087
The dominated convergence theorem
A dominated pointwise limit may be integrated term by term.
T-088
The Fubini–Tonelli theorem
When iterated integrals may be exchanged.