
Theorem
41: 
Holder inequality 

Theorem
42: 
CauchySchwarz inequality [first] 

Theorem
43: 
Minkowski inequality 

Theorem
44: 
Absolute Convergence in Lp 

Theorem 45: 
Extraction of almost sure limit in Lp 

Theorem 46: 
Lp is complete 

Theorem 47: 
Convergent subsequence in compact metric space 

Theorem 48: 
Compactness criterion in Rn 

Theorem 49: 
Rn and Cn are complete 

Theorem
50: 
CauchySchwarz inequality [second] 

Theorem
51: 
Rn and Cn are hilbert
spaces 

Theorem
52: 
Projection on a closed and convex subset 

Theorem
53: 
Orthogonal projection 

Theorem 54: 
Bounded linear functional as innerproduct 

Theorem 55: 
Bounded linear functional in L2 

Theorem 56: 
Permutation property implies absolute convergence 

Theorem 57: 
Total variation is a finite measure 

Theorem 58: 
Absolute continuity criterion between measures 

Theorem
59: 
Integral average lying in closed subset of C 

Theorem
60: 
RadonNikodym theorem for complex measure 


