
Theorem 1: 
Dynkin system theorem 

Theorem 2: 
Extension of a measure from a semiring to a ring 

Theorem 3: 
Outermeasure is a measure on its sigmaalgebra 

Theorem 4: 
Caratheodory extension theorem 

Theorem 5: 
Extension of a measure from a semiring to a sigmaalgebra 

Theorem 6: 
A generator of the borel sigmaalgebra on R 

Theorem 7: 
Upward continuity of a measure 

Theorem 8: 
Downward continuity of a measure 

Theorem 9: 
Stieltjes measure on R 

Theorem 10: 
Trace theorem 

Theorem 11: 
Stieltjes measure on R+ 

Theorem 12: 
Induced metric theorem 

Theorem 13: 
R is metrizable 

Theorem 14: 
Measurability criterion 

Theorem 15: 
Measurability criteria 

Theorem 16: 
Convergence criterion in R 

Theorem 17: 
Measurability of limit 

Theorem 18: 
Approximation by simple functions 

Theorem 19: 
Monotone convergence theorem 

Theorem 20: 
Fatou lemma 


