Fix a point ac E RR and define for each Borel set I C TR} | 1 if* E E 10 if * * E a ) Prove that Ox is a measure . b ) Prove ( from definitions )...

Please help me prove the following about Borel measurable functions

Fix a point ac E RR and define for each Borel set I C TR}| 1 if* E E10if * * Ea ) Prove that Ox is a measure .b ) Prove ( from definitions ) that for every Borel measurable function f : R -*10 , too) .f dox = f ( 20 ) .