Definition of Outer measure II HINDI II MEASURE THEORY скачать в хорошем качестве

Definition of Outer measure II HINDI II MEASURE THEORY

Please Donate Money ('' Shagun ka ek rupay'') for this Channel pay Rs 1 on google pay UPI id 83f2789@oksbi Example on outeb measure to clear your doubt :-    • Example of Outer measure   HELLO GUYS, I Hope u like this video if u didn't understand another video will definitely helps to clear your all doubts trust me , make sure you watch entire video    • Outer measure ( for better understanding)   Let I be a nonempty interval of real numbers. We define its length, £(1), to be 00 if I is unbounded and otherwise define its length to be the difference of its endpoints. For a set A of real numbers, consider the countable collections (h}~l of nonempty open, bounded intervals that cover A, that is, collections for which A ~ U~l h. For each such collection, consider the sum of the lengths of the intervals in the collection. Since the lengths are positive numbers, each sum is uniquely defined independently of the order of the terms. We define the outer measure3 of A, m*( A), to be the infimum of all such sums, that is It Other realted queries What is outer measure Hindi explanation of outer measure Outer measure in Hindi Outer measure in lebesgue measure Outer measure for Msc mathematics Outer measure for statistics Outer measure in real analysis Outer measure Royden Easy definition of outer measure What is outer measure in Hindi Outer measure for higher mathematics outer measure in statistics what is outer measure for Msc statistics #outermeasure #realanalysis #measuretheory #lebseguemeasure #mscmathematics #statistics #exampleonoutermeasure #skclasses #puneuniversity #mit Let I be a nonempty interval of real numbers. We define its length, 1(I), to be oo if I is unbounded and otherwise define its length to be the difference of its endpoints. For a set A of real numbers, consider the countable collections {Ik'1 of nonempty open, bounded intervals that cover A, that is, collections for which 1 Ik. For each such collection, consider the sum of the lengths of the intervals in the collection. Since the lengths are positive numbers, each sum is uniquely defined independently of the order of the terms. We define the outer measure3 of A, m* (A), to be the infimum of all such sums, that is m*(A) = inf I(Ik) 1k=1 It follows immediately from the definition of outer measure that m* (0) = 0. Moreover, since any cover of a set B is also a cover of any subset of B, outer measure is monotone in the sense that if ACB, then m*(A) m*(B).