Example of Outer measure

What is cover:- • Cover :- How union of ...
What is length :- • Length of an Interval...
Definition of outer measure:- • Definition of Outer me...
What are the example of outer measure
Example on outer measure
Hindi explanation of example on
outer measure
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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 A C U' 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
ACCUHIk .
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
ifACB, then m*(A) m*(B).

[@thenewdimension9832]

Love u sir 💖

[@PathFindersAcademy]

Thanks a lot ur message really creates a new dimensions for Creator.....

[@bharatnakum9286]

Vah🎉🎉🎉 very nice Sir...... Example with definition
Keep it up.... 🥇🥇🥇

[@PathFindersAcademy]

Keep watching 😍

[@tanuja_adhikari]

Easy and nice explanation 😅thanks a lot sir🙏🏻🙂

[@bprasadstar1]

You explained it well sir. 5:09 mein 0 k LHS mein 0.9999.. nahi hoga shayad.

[@aditichandel5367]

Good work...The definition is very confusing..but the examples that u took really helped me to understand it

[@PathFindersAcademy]

Glad it helped!

[@mynajafee3360]

Sir playlist se hi hokar aya hu

[@cvraman5908]

Lovely

[@arliemagbanua4257]

great explaination,can you send me notes related to lebesgue measure :union of dijoint interv als.thank you

[@realmathsview3602]

Good

[@HarpreetSingh-ke2zk]

For what purpose do we require outer measure?

[@MuhammadBilal-pi3lo]

best.

[@poonitasharma9809]

Thanks sir for a good explanation and clr this topic

[@PathFindersAcademy]

Welcome!!!

[@ArvindKumar-qd9zk]

Best explanation

[@PathFindersAcademy]

Glad you think so!

[@gurshaankaur6285]

Thank u soo much sir for such an easy explanation 👌👌😇

[@PathFindersAcademy]

Most welcome 😊

[@pravinsahu2429]

A measurable function is continuous . It is true or false ? Please batana ok

[@pravinsahu2429]

Es ko bhi batana

[@allinoneentertainment948]

Yes

[@allinoneentertainment948]

True

[@zunnurainzunnurain7085]

Well explain sir....

[@PathFindersAcademy]

Thanks and welcome

[@pravinsahu2429]

The outer measur of a finite set is..........

[@PathFindersAcademy]

Zero because as every finite set can be written as union of Singleton set
As outer measure of Singleton set is zero
By subadditve property (I made this video)
Due to this...

[@pravinsahu2429]

@@PathFindersAcademy thank you

[@kindykomal]

Million Thanks . Great work 🙏🏻👍😇

[@PathFindersAcademy]

You're most welcome

[@jairoselin5119]

Thank you

[@PathFindersAcademy]

Welcome!

[@Easymath158]

Best explaination

[@PathFindersAcademy]

thanks

[@alokkar1682]

Superb

[@PathFindersAcademy]

Thanks 🤗

[@archanap8718]

Super sir

[@PathFindersAcademy]

Thanks a lot....

[@mynajafee3360]

Sir yaha p summation k role to apne bataya hi ni

[@PathFindersAcademy]

Syhd dusare video Mai hoga ek baar playlist check kro,...

[@vikas7979]

bhai summation se hi to intervals ka sum kr rhe