Minkowski's inequality

[@-InsanelySick-]

I appreciate the effort you put in those videos, it's tough to find theoretical math explained this clearly on youtube. Do you have (or plan on releasing) any video tutorials about the Lebesgue integral? I couldn't find it explained clearly anywhere! Patricularly the initial construction of the measure and the whole concept of sigma algebras and Borel sets seems really alien to me.

[@brekipalsson9759]

Your videos are clear and understandable, good job!

[@amosemarshall]

Dear Chris, I really liked the way you used the length function(p-norm of finite space) to prove the inequality. But could you help me in proving Minkowski's Inequality without using Holder's Inequality. Thank you.
Warm regards,
Marshall

[@muhammadsaqibarshad4427]

That's very helpful for me. God bless you with a better reward.

[@lbomcarvalho]

Great explanation. Congratulations. Can you provide the pdf where both demonstrations appear?

[@curous65]

From 9:08 - 9:16 - I have a doubt. The Holder's inequality has modulus of product of two vectors while the Right Side of eqn (7) has product of modulus of vectors. Can we still apply Holder's inequality as you have shown ? Is it correct ?

[@DrChrisTisdell]

@Azuresong i hope to cover these topics one day, but not anytime soon. I am now experimenting with connections between my research and teaching - that's why I've posted this particular video, because I use it in my latest research results.

[@zahrazahra-lm4jx]

I want the minkowski inequality when 0 < p < 1

[@the_informative_edge]

​@@zahrazahra-lm4jxMuch needed demand. I need this one

[@the_informative_edge]

@DrChrisTisdell please upload the proofs for Holder's & Minkowski's inequalities..

[@primefactor5417]

Professor , please make more videos on metric spaces ...

[@hasanmosharrof]

great explanation. Would you please explain if p

[@leof9849]

sir this video is magnificent, and i have a small request that u present a video with a compilation of olympiad inequalities.(for a high school student as i am in 9th standard in india),i know it will take up your valuable time but we will be highly helped and i will be much obliged.thanks in advance.(your video of fourier series was just magnificent)
(MildorfInequalities.pdf gives the list of olympiad inequalities)

[@fcmitroi]

Dear Chris,
Please see
Minkowski, H. Geometrie der Zahlen, Vol. 1. Leipzig, Germany: pp. 115-117, 1896. for reference.
Best regards.

[@farazfarooqi4675]

Sir, I have great difficulty in solving the back questions of every chapter in the functional analysis book by Kreyszig. Please advise me on how I can overcome this problem.

[@muhammadsadiq1792]

Sir why we are not used minkoski inequality for(0,1)

[@technoguyx]

You can prove by counterexample that the inequality is not true for p∈(0,1) - pick numbers smaller than 1 for instance. This is also why the p-norm is only a norm in ℝⁿ for p≥1.

[@mathildelouviot]

Thanks from France ! :)

[@DrChrisTisdell]

Hi - good question. We are multiplying real numbers (not vectors) in the summands. So |c*d| = |c|*|d| and its all OK.

[@juancorderoromero6610]

Very interesting!! thanks for the video again

[@DrChrisTisdell]

My pleasure!

[@maryamkhan9753]

great explanation... good job!

[@DrChrisTisdell]

Great! I see you have some really useful vids!!

[@jonathannissim2774]

Thank you sir! Still very useful!

[@mpendulocele9548]

Great video thanks a lot.

[@LeavingCertMaths]

Interesting. Thanks.

[@benjaminhu2136]

Thanks for the video :))

[@이서진-p7m]

Thank you sir

[@prafullkakde6508]

sir i am form india , may you provide pdf of these therorm

[@oumaima1214]

Thank you🤎

[@ahlamelbojaddaini2218]

Can i get your e-mail sir?

[@DrChrisTisdell]

@fcmitroi Excellent - thank you!

[@SuperApokalips]

that pretty nice