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Please Donate Money ('' Shagun ka ek rupay'') for this Channel pay Rs 1 on google pay UPI id 83f2789@oksbi phone pe UPI id : 8698496936@ybl union of two measurable sets is again a measurable set. Theorem Let E1 and E2 be two measurable sets, then E1 ⋃E2 is measurable. WE have two measurable set say E1 and E2. we have to prove that union of these two measurable sets i.e. E1 U E2 is again measurable . to prove that the union is measurable it is sufficient to prove that one inequality (why this inequality E is measurable iff this inequality holds • E is measurable set iff this inequality ho... ) lets go for the proof using the definition of measurable set on E1 for any set say E1 and then using the definition of measurable set on E2 for any set say A-E1 Compliment and then putting in each other and by applying countably sub additive and set theory identities outer measure is countably subadditive :- • Propostion 3 : Outer measure is countably... LIKE COMMENT SHARE SUBSCRIBE If u have any doubt regarding to this video let me know in the comment box #realanalyis #measuretheory #puneuniversity #university #Msc #higherstudies