cond.meas-prob - Conditional probability & conditional...

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Unformatted text preview: Conditional probability & conditional measures Jonathan L.F. King University of Florida, Gainesville FL 32611-2082, USA squash@math.ufl.edu Webpage http://www.math.ufl.edu/ squash/ 4 May, 2010 (at 23:20 ) Abstract: Abs. cty, Radon-Nikodym thm. Elementary martingale thy. In progress: As of 4May2010 Bonjour. As additional notation 1 use to mean identically equals ; on the probability space, we mean this a.e. Use r.var or r.v for random variable . Use r.walk for random walk . Sets & Fields. Use for is an element of. Letting P be the set of primes, then, 5 P yet 6 / P . Changing the emphasis, P 3 5 ( P owns 5 ) yet P 63 6. For subsets A and B of the same space, , the inclusion relation A B means: A , necessarily B 3 . And this can be written B A . Use A $ B for proper inclu- sion, i.e, A B yet A 6 = B . The difference set B r A is { B | / A } . Employ A c for the complement r A . Use A 4 B for symmetric 1 Phrases: WLOG : Without loss of generality . TFAE : The following are equivalent . OTForm : of the form . FTSOC : For the sake of contradiction . Use iff : if and only if . IST : It Suffices to as in ISTShow , ISTExhibit . Use w.r.t : with respect to and s.t : such that . Latin: e.g : exempli gratia , for example . i.e : id est , that is . Number Sets: An expression such as k N ( read as k is an element of N or k in N ) means that k is a natural number; a natnum . N = naturalnumbers = { , 1 , 2 ,... } . Z = integers = { ...,- 2 ,- 1 , , 1 ,... } . For the set { 1 , 2 , 3 ,... } of positive integers, the posints , use Z + . Use Z- for the negative integers, the negints . Q = rationalnumbers = { p q | p Z and q Z + } . Use Q + for the positive ratnums and Q- for the negative ratnums. R = reals. The posreals R + and the negreals R- . C = complex numbers, also called the complexes . Mathematical objects: Poly(s) : polynomial(s) . Irred : irreducible . Coeff : coefficient and var(s) : variable(s) and parm(s) : parameter(s) . Expr. : expression . Fnc : function (so ratfnc : means rational function , a ratio of polynomials). Seq : sequence . Soln : solution . Propn : proposition . CEX : Counterexample . Eqn : equation . RhS: RightHand Side of an eqn or inequality. LhS: lefthand side . Sqrt : square-root , e.g, the sqrt of 16 is 4. Cts : continuous and cty : continuity . Ptn : partition , but pt : point , as in a fixed-pt of a map....
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This note was uploaded on 01/26/2012 for the course MAP 6472 taught by Professor King during the Fall '11 term at University of Florida.

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cond.meas-prob - Conditional probability & conditional...

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