###### Let C be a set in three – dimensional space and let @ ( C ) be equal to the volume of C , if Chas finite* volume ; otherwise , let Q ( O’; be…
September 3, 2020
###### lt; lt; Question 10 of 18 Discretionary spending Automatic stabilizers Answer Bank Widespread layoffs trigger an increase in government spending on…
September 3, 2020

Please help with Probability Space functions. The problem is shown in the attachment. I was struggling in understand the concept and I’ll be grateful if you can show me the steps to solutions. Thanks in advance!

1 . If C 1, CZ, C3 . …. are sets such that Cr C Ch+ 1 . K = 1, 2, 3 . …. limk_ too CR is defined as theunion C , UC 2 UC , U …. Find lim k_ too CK.( 2 ) CK = Lac ER : 1 / K &lt; &lt; &lt; 3 – 1/ Kj , K = 1, 2, 3 , … .( b ) Ck = ( ( 2 , 4 ) ER 2 : 1 / k &lt; 2 2 + y 2 { 1 – 1 / K} , K = 1, 2, 3 . … .2 . If C 1 , C2, C3 . …. are sets such that ( * ) Ck+1 . K = 1 , 2 , 3 . … . limk_ too CR is defined as theintersection CIn Cz N C; M …. Find limk_ too CK.( a ) CK. = {` ER : 2 – 1 / K &lt; &lt; &lt; 2) , K = 1, 2, 3 . ….( b ) Ck = { ER : 2 &lt; &lt; &lt; 2 + 1 / K; ] , K = 1 , 2, 3 , … .( C ) Ck = ( ( 2 , 4 ) E RR 2 : 0 &lt; 2 2 + y ? &lt; 1 / K;] , K = 1, 2, 3 . ….3. For every one- dimensional set C , define the function @ ( C ) = &gt; of (a ) , where f (a ) – 12/ 31 ( 1/ 3 )2 .I = 0. 1, 2. …. zero elsewhere . If ( 1 = 12 : 2 – 0. 1, 2, 31 and C 2 – 12 : 2 – 0, 1, 2…. ], findQ ( ( 1 ) and Q ( ( 2 ) . Hint : Recall that S = at art … + arn- 1 = a ( 1 – pro ) / ( 1 – 8) , and hence , itfollows that Jim ~ _ too S = a / ( 1 – 7 ) provided that | ~| &lt; 1 .4. Let C be a set in one- dimensional space and let @ ( C ) be equal to the number of points in C’ whichcorrespond to positive integers . Then Q ( C ) is a function of the set C . Find @ ( C ) .( 2 ) C = PIER : 0 &lt; &lt; &lt; 5).( b ) C = 6 – 2, – 1} .( C ) C = LIER : – 00 &lt; &lt; &lt; 6}.