Transcription of 6. Product Spaces - Probability
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6. Product Spaces - Probability
Tutorial 6: Product the following,Iis a non-empty 50 Let( i)i Ibe a family of sets, indexed by a non-empty productof the family( i)i Itheset, denoted i I i, and defined by: i I i ={ :I i I i, (i) i, i I}In other words, i I iis the set of all maps defined onI,withvalues in i I i, such that (i) ifor alli (Axiomofchoice)Let( i)i Ibe a family of sets,indexed by a non-empty , i I iis non-empty, if andonly if iis non-empty for alli finite, this theorem is traditionally derived from other 6: Product Spaces2 Exercise Let be a set and suppose that i= , i Iinstead of i I i. Show that Iis the set of allmaps :I .2.
Tutorial 6: Product Spaces 5 Definition 53 Let (Ω i,F i) i∈I be a family of measurable spaces, in- dexed by a non-empty set I.Wecallmeasurable rectangle,any rectangle of the family (F i) i∈I.The set of all measurable rectangles
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