Refinement of Partition | Theorem | The Riemann Stieltjes sum | Effects of refinement on r-s sums

Theorem of Refinement of Partition | Refinement of partition and its effect on Riemann Stieltjes sum | Riemann stieltjes sums | Lower Reimann Stieltjes Sum | Upper Riemann Stieltjes Sum | The R-S Integral | Real analysis | OMG Maths | Classes By Cheena Banga. | #omgmaths
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***The Riemann-Stieltjes Integral***
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The Riemann-Stieltjes Integral
The R-S Integral
Limit and Continuity
Limit Inferior and limit superior definition and theorems
Cauchy Sequence in Compact Metric Space is Convergent
nth tail of sequence
Tail of a sequence
P Series Test for convergence of series
Limit Comparison Test for Convergence
Cantor Intersection Theorem
E is a subset of metric space X then Diameter of closure of E is equal to Diameter of E
Cauchy First theorem on limits
Bolzano Weierstrass Theorem
Every bounded sequence has a convergent sub sequence
Every Cauchy sequence is a Bounded sequence
Every convergent Sequence is cauchy sequence
Cauchy Sequence
Cauchy Sequence Definition
Cauchy Sequence theorems
Sub sequence of a sequence
Algebraic Properties of Limits
Algebra of limit of sequence
Properties of limit
limit laws of sequence
sandwich theorem
squeeze theorem
Sequence and series
real sequence
range of sequence
constant sequence
uniqueness theorem
Sequences in metric space
limit of sequence
Convergent sequence
Every connected subset of R is an interval
The Real line R is connected
Every interval is connected
In R, intervals and only intervals are connected.
A subset E of R is connected iff E is an interval
compactness in Real Analysis
Connectedness in Real Analysis
Compactness in topology
Connectedness in topology
compactness
connectedness
theorems of compactness
theorems of connectedness
Heine-Borel theorem
Closed Set | definition | theorems
set is closed iff its complement is open
Bolzano weierstrass theorem : Every infinite bounded subset of R has a limit point.
Definition of Neighbourhood of a point
Definition of Open set
infinite intersection of open sets need not to be open
Union of two NBDS is NBD
Intersection of NBDS is NBD
Superset of a NBD is also a NBD
Every Open interval (a,b) is neighbourhood of each of its points.
Closed interval is neighbourhood of each point except end points.
real numbers is NBD of each real number
Rational numbers set is not the neighbourhood of any of its points.
Metric space | Distance Function | Example
Metric space : Definition and Axioms
Real Analysis : Introduction and Intervals
Union of countable sets is countable
Finite,infinite,equivalent,denumerable,countable sets
Infinite subset of countable set is countable
Field,Ordered Field,complete Ordered Field
Set of Integers is Countable
Supremum and infimum
Set is countably infinite iff it can be written in the form distinct elements
Continuum Hypothesis
Cartesian product of two countable sets is Countable
Set of Rational numbers is Countable
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Definition of metric Space
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connectedness
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isometries
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notions of metric space equivalence
Topological properties
Distance between points and sets
Hausdorff distance and Gromov metric
Product metric spaces
Continuity of distance
Quotient metric spaces
Generalizations of metric spaces
Metric spaces as enriched categories

[@OMGMaths]

You can download PDF from:
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Related Playlist:The Riemann Stieltjes Integral
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[@ashishkoreti6254]

You are so great mathematician mam ✍️✍️✍️📚📚📚

[@OMGMaths]

Glad it was helpful 😊
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[@JyotiSaini-4639]

Thanku mam❤❤
I am facing very difficulty with this topic but still now i understand!!!!

[@OMGMaths]

Glad to hear

[@geethamangalathu]

Thank you so much for these videos. I was struggling a lot to get the real analysis videos. So many videos were there but was not able to understand the concept. This is very clear.
If i could get some bounded variation videos it will be great. Thank you once again.

[@creativevision632]

Great mam...!
I understood in first time with your style..
Thanks❤🙏

[@OMGMaths]

Thank You 😊 Your appreciation means a lot lot for me….Please write your valuable reviews at g.page/r/CRP90Pt3uFhFEAg/review
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[@ashishkoreti6254]

Thank you for explaining so well!!!🎈🎈🎈

[@OMGMaths]

Glad it was helpful 😊
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[@anojkumarsah605]

Appreciable effort , understandable..... Keep growing 👍

[@Shrimad_BhagwatGita]

Ma'am (5:8) timing pe aapne btaya ki 'j' ki value '1' and 'n' k bich m ya equal m vary kr skti hai
But jb 'j' ki value 1 put Kareinge to x(j-1) ki value ' x° ' k equal ho jayegi
But partition m aapne btaya tha ki values increasing order m hoti hain .
To partition k bich m infimum value kaise aa rhi hai interval ki?

[@amallcreation4131]

thanks for detailing teaching ma'am .keep it up🥰

[@OMGMaths]

Thank You 🙏 We are working on Vedic Maths Please check the playlist for vedic maths course and share with others. th-cam.com/play/PLYisSyPLgRv4pwh8PxWLbHPzAfQdo8EQ0.html

[@asharma1912]

Thank you so much mam aapki video dekhkar mere bohot achen marks aayen...love you mam 😊

[@OMGMaths]

My Pleasure 😊 Your appreciation means a lot lot for me….Please write your valuable reviews at g.page/r/CRP90Pt3uFhFEAg/review
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[@shameemaumar1667]

Thank u so much
Very very help ful

[@Pankaj-eq8ru]

Thank you ma'am 🙏🙏

[@kavitajoshi4539]

Mam aap bahut achaa parate h...... Plzzz or sub. jaise abstract complex ke v video banaye plzz msc me bahut help hoti h🙏🙏

[@OMGMaths]

Thank You 🙏 Subscribe th-cam.com/users/OMGMaths and press 🔔 for notifications. Please write your valuable reviews at g.page/r/CRP90Pt3uFhFEAg/review
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[@shwetaSingh-ft9fi]

Thank you very much sis

[@jagan1137]

Mam pls use symbols n notations from principle of mathematical analysis, walter rudin

[@ThomasAgc]

Thankyou so much mam

[@prathamkumar7224]

Finally, I could understand...🙏🙏

[@kokilkoiri9071]

Aapane bahut achcha bataya ma'am.thank you so much

[@OMGMaths]

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[@yashvantgurjar5257]

Ok thanks u give me response but stil I confuse that why any one not explain taking X Y plane / secondly if unction is monotonic

[@OMGMaths]

Please watch this video I hope you will understand the concept
th-cam.com/video/_T7jZv5MzAE/w-d-xo.html

[@yashvantgurjar5257]

@@OMGMaths ok

[@VamsiKomotipalli]

Thank u

[@muhammadail3709]

Thanks very much

[@yashvantgurjar5257]

Please tell me infm and supm are value of function along Y axis yes or no

[@OMGMaths]

Yes because we are taking values of f(x)

[@gaganpreet_kaur2496]

Mam please upload a video of sturm liouville boundary value problem theorem and sum. Ur video is very useful for us. 🌹

[@OMGMaths]

Will try to upload required video asap…
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[@SANOJKUMAR-eh1jj]

Thakns you so much maam ❤❤🙏🙏🙏🙏

[@OMGMaths]

It's my pleasure 😊
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[@shubhamrawat6551]

Mam..
Is video ki pdf bhi mil jayegi

[@OMGMaths]

pdf link : omgmaths.com/real-analysis/refinement-of-partition-and-its-effect-on-r-s-sums-theorem-of-refinement-of-partition/

[@Raghava14344]

Really it is like poetry

[@bankerAsh]

Superb ma'am

[@OMGMaths]

Thank You 😊 Your appreciation means a lot lot for me….Please write your valuable reviews at g.page/r/CRP90Pt3uFhFEAg/review
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[@ramkarankhichar2623]

Thak you so much mam like a mom🤗

[@OMGMaths]

Thanks for appreciation…. Please write your valuable reviews at g.page/r/CRP90Pt3uFhFEAg/review
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[@quratulainquratulain3633]

Thanks you so much video kay lay

[@ANANDVERMA-wo8if]

Helpful video mam 👌👌👌

[@OMGMaths]

Thank you 😊 please Like and Share
find more videos on R-S Integral here th-cam.com/play/PLYisSyPLgRv605svWrFolryHcjlF6lDgU.html

[@AbhishekRatna-ug3jz]

22:38 LINE NO. 1 ME mj hai hi nhi z valefuntion me tb fir vha 2nd line me kese aagya

[@Pankaj-eq8ru]

Ma'am kya msc ki complete syllabus ki video bna rkhi h kya

[@OMGMaths]

“Real Analysis” only

[@Pankaj-eq8ru]

@@OMGMaths ok ma'am
Real analysis ki sari videos uploaded h ma'am

[@jyotichauhan3478]

Mam aap bhut accha pedhati ho

[@WalkinTech]

Ma'm iska second part krke uske pdf attach kr dijiye.🙏

[@allinonenumberone]

Mem refinement me g hai or Xg or z hai 🙄

[@ALLINONE112]

Keep it up mam.

[@OMGMaths]

Thank You 🙏
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[@yashvantgurjar5257]

monotonic increasing function

[@shashank_kishore_]

❤❤❤❤❤❤❤❤❤❤❤❤❤

[@radhikamaurya3550]

Phir se refinement ke bare me batae

[@shekharpradhan5576]

Thank you ma'am.