<P>这是德州的<FONT face=Georgia><b>Max Stinchcombe</b> 教授的讲义，下面是目录</FONT></P>
<P>1. Introduction.
2. Sequence Spaces: These are the crucial mathematical constructs for the limit
theorems that are behind learning theory. Deterministic dynamic systems give
rise to points in sequence spaces, statistical learning and stochastic process
theory can be studied as probabilities on sequence spaces.
3. Metric Spaces:
(a) Completeness, the metric completion theorem.
(b) Constructing R and Rk.
Detour: the contraction mapping theorem; stability conditions for
deterministic dynamic systems; exponential convergence to the unique
ergodic distribution of a nite, communicating Markov chain; theexistence and uniqueness of a value function for discounted dynamic
programming.
(c) Compactness.
Detour: Berge's theorem of the maximum; continuity of value functions;
upper-hemicontinuity of solution sets and equilibrium sets.
(d) Fictitious play and Cesaro (non-)convergence in Rk.
4. Probabilities of elds and - elds:
(a) Finitely additive probabilities are not enough.
Detour: money pumps and nitely additive probabilities; countably
additive extensions on compacti cations, [25].
(b) Extensions of probabilities through the metric completion theorem.
Detour: weak and norm convergence of probabilities on metric
spaces; equilibrium existence and equilibrium re nement for compact
metric space games.
Detour: convergence to Brownian motion; a.e. continuous functions
of weakly convergent sequences; limit distributions based on
Brownian motion functionals, [6].
(c) The Borel-Cantelli lemmas.
(d) The tail - eld and the 0-1 law.
(e) Conditional probabilities, the tail - eld, and learnability.
(f) The martingale convergence theorem.
5. Learning in games.
(a) Kalai and Lehrer [14] through Blackwell and Dubins' merging of opinions
theorem, Nachbar's [18] response.
(b) Hart and Mas-Colell's [10] convergence to correlated equilibria through
Blackwell's [4] approachability theorem.
(c) Self-con rming equilibria [9] of extensive form games.
(d) The evolution of conventions, Young [28] and KMR [16] approaches, Bergin's
[2] response.
(e) Evolutionary dynamics and strategic stability [20].
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