Proposition 2 : Outer Measure is translation Invariant скачать в хорошем качестве

Proposition 2 : Outer Measure is translation Invariant

Please Donate Money ('' Shagun ka ek rupay'') for this Channel Measure theory playlist:-   • MEASURE THEORY   To prove this we need to know something i.e. Length of Interval is translation invariant Like Dislike comment. share follow me on Instagram:- @kulsanketkumar other related query outermeasure is translate invartiant prove that outer measure is translate invariant proof of outer measurte istranlation invariant hindi translation doesn't effect outermeasure #measuretheory #skclasses #puneuniversity #lebesguemeasure #realanalysis #hindi #outermeasureistranslteinvariant #mscmathematics #delhiuniversity #ugc Proposition 2 Outer measure is translation invariant, that is, for any set A and number y, m*(A + y) = m*(A). Proof Observe that if {Ik}k 1 is any countable collection of sets, then {Ik}k01 covers A if and only if Ilk + y}k 1 covers A + y. Moreover, if each Ik is an open interval, then each Ik + y is an open interval of the same length and so 00 00 I1(Ik)=I1(Ik+Y)- k=1 k=1 The conclusion follows from these two observations. Translation Invariance of the Lebesgue Outer Measure