6HiDg Math As disused test the X stnke We a Fi Df If : X this , B PI , , Swf . , , Ez Ext , @ Psg ht : A PH ) I . HW Therefore is , . it tns at to . . f here algebra :c EX then , , . Et . . Ez , . . ( Eict . Et . s be o a a same So , ) =µW HE be maslle ( cbrdwdr if comthle / ul E) ) - µlE since Bmeaxbk EEX VF , . V. , A fsbab f inning then , . . ) X µlEi = tht so Edt tnl . . . gin - : ) ( dead web cnpkmutkr ) intraday Ezn E, n , . . ( = . E, u A smarty ) sme 1 the abehm rabeh B trial o . a ( possibly o - abehn X on . . . ' ) En = A e E ' e & A X= Eu As 3 EEA EB . ) ) mcontlde ) alsek Ezv 0 ( the date rabk index set any colledtn ) , thick exits s ad amnesty waedsn 3 Et . . shld . . X on E , UEZU , . algebra - µ(E4=n( since EUEU o a at X shed be mbsnble & , freak AEI . scope a o - abek on a at X then . . Dt . the umet be arbitrary which sheets specify X & ff±A£ PI sits need to we . X on 0 Eet {0 mere a , , 0 mantle Me the marble also be . . . EEA For E. For 2 E. , , E For contains For D : . he dsid cmdr conthle is 2 E rdydm A A want to define we The colbeth of meaty st then , a 2 D shdd if 1 Props stwhemt Xie = Abo uhih an . iht guns st X a to be measurable goy are gin , E of intmdhf all rafcbms subsets arty of { X , there is lwhihexb . a since unique smallest { c- PCD r whih , - abdn Bao - M ( E) abek ) containing MK ) E. . Balled the . o . ab . Ml E) generated by E . Remit A : o algebra . yaid D fan expect other words In special a addilm . The . is A multiplicate klutz is X gewtl see s = On 10 ) then ( X A) , The menu 5 - E. , 13 a . . . . Et N# Et : D measuke in ( counting Ext ( Din . Ft . muse buntzy the a if finite is pevios Lexwb more × . the axing ×=× H× . : ) UN ) in in use . on B* IX A) an tpologil space X a f Bx Ekmb . measure , & uk ) < & degenerate use & an = : X . , if A- ml . f A dents events are disjoint the parwk ) ht A =P K) uflft B satisfy rigs w/ are , hw ndditk am to generate ( uhih ° which D , alld Bad are sets the X an o - B× abdm . , is a E , UE , [ 0, D nits mp where sit define ( E) µ P (D = Define . ipliy hare nk ) IEI this . E) 8×1 [ o , D µ . ) UIE = , tiled ) + . . . IX A ) D Again , this is a The triple , is 1 El < tt x EA is ) n a music space . . deaf none a . to { i%a⇐ = Et E , 1) = E t x - f :X & . . obviously µ( E) v. measure sets are always we hit A- PIA & due XEX may ( = . space needed to rule at the is :b is X on ways A are ( In pokhilitg kymze , mumble sit : adv D: rigs whit Boolean thy by the Bard rabdm B A algdm rig a to correspond & ^ o . E, Far 2 wl set a algebra 1.2 far eqmwbt Proposition ht X be - sets alhdn of per the by o algebras B tooth w/ garths st a n & a is A MX 0 exaple of important , difference 3 the symmetric - The most whit Boolean additne idnhz is The . fabeka a multiplication . try In . algebra into tnn am a bogie symbolic we , f use Boden a . measure . fndtn then , ×%⇐fk) County the fdn none wnypls fly ) = { 1 0 to the oghtffy fly ) if y=x else . = 1 tt EX & Dire y , nose corresponds to .