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jk.class - Class Notes for Probability Potential Theory...

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Class Notes for Probability & Potential Theory : Probability Jonathan L.F. King University of Florida, Gainesville FL 32611-2082, USA [email protected] Webpage http://www.math.ufl.edu/ squash/ 21 October, 2003 (at 21:16 ) Notation. WLOG : ‘ Without loss of generality ’. TFAE : The following are equivalent ’. FTSOC : ‘ For the sake of con- tradiction ’; sometimes written as FTSOContradiction . IST : It Suffices to ’, as in ISTShow , ISTExhibit . iff : ‘ if and only if ’. s.t : ‘ such that ’. t.fol : ‘ the following ’. Mathematical objects: fnc : function ’. seq : sequence ’. soln : solution ’. prop’n : proposition ’. CEX : Counterexample ’. eqn : equation ’. RHS: RightHand Side of an eqn, inequality. LHS: lefthand side ’. var(s) : variable(s) ’. parm(s) : parameter(s) ’. poly(s) : polynomial(s) ’. r.var , or r.v: ‘ random variable ’. Prolegomenon Our probability space is Ω := ( Ω , F , P ) . A r.v.seq ~ S is Cauchy in probability , written P - Cauchy , if: ε, δ so that for all large j

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