Master Dissertation

The Inductive Construction of Tn(x1, . . . , xn).
1. Assume Tm(x1, . . . , xm) for 1 ≤ m ≤ n − 1 are known.
2. Construct advanced and retarded distributions as follows
A ′ (x1, . . . , xn) =
˜Tn1 (X)Tn−n1 (Y, xn) (5.7)
P2
R ′ (x1, . . . , xn) =
P2
Tn−n1 (Y, xn) ˜ Tn1 (X) (5.8)
where P2 is the set of all partitions {x1, . . . , xn−1} = X ∪ Y , X = ∅
and n1 = |X| ≥ 1.
3. Include the empty set ∅ as follows
A(x1, . . . , xn) =
˜Tn1 (X)Tn−n1 (Y, xn)
P 0 2
= A ′ n(x1, . . . , xn) + Tn(x1, . . . , xn) (5.9)
R(x1, . . . , xn) =
Tn−n1 (Y, xn) ˜ Tn1 (X)
4. The difference is
5. Now
P 0 2
= R ′ n(x1, . . . , xn) + Tn(x1, . . . , xn). (5.10)
Dn = R ′ n − A ′ n = Rn − An. (5.11)
Tn = Rn − R ′ n = An − A ′ n. (5.12)
We thus need to determine either Rn or An. This will be done by
investigating the support properties of the distributions.
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