Exploring the Mysterious "Sets with Mass Zero

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In summary, Sets with measure zero are interesting, and a good introduction to measure theory can be found in Measures, Integrals and Martingales by R. Schillingwell.
  • #1
sutupidmath
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where to find??

well, some people told me that "Sets with Mass Zero" are quite interesting, btw i have no idea what they are, but i could not find anything related to them. So could anyone recommend anything online about these??
 
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  • #2
Are you sure it isn't supposed to read "Sets with measure zero" ?
 
  • #3
CompuChip said:
Are you sure it isn't supposed to read "Sets with measure zero" ?
Maybe, i don't know, but i think it might be what i am looking for. Btw i just translated the "title" from my language to English.
 
  • #4
btw. i found wat i was looking for. Like you said CompuChip, it is Sets with measure zero. thnx
 
  • #5
well, i would like to know what backgroud in mathematics one should have to be able to fully understand "sets with measure zero", because they just seem to be out of my league for the moment. Btw Calculus I is all i got at the moment.
 
  • #6
If you really want to understand them you should take measure theory. In my curriculum, it was a third year course, though I actually think you don't need much more than some analysis (mainly: convergence and Riemann integration). A good introduction which doesn't require much knowledge is Measures, Integrals and Martingales by R. Schilling
 
  • #7
well i haven't yet gotten into any university, i am going to be a freshman this fall. However, i am going to have a look at this
http://www.mathematik.uni-marburg.de/~schilling/measures_integrals_and_martingales/index.html


Will this be helpful?
 
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  • #8
That's the book I meant. In my opinion, it's very accessible and doesn't require much knowledge (at least, for the first 10 chapters or so). If you want to go through all the proofs step by step, you might need a little more than Calc I, but in general I think you should be able to get the point.
Although, after three years of university level courses, I may underestimate the level. You can buy the book anyway, skim through it; in two or three years, you can always read it again and go through the details.
 

FAQ: Exploring the Mysterious "Sets with Mass Zero

What are "Sets with Mass Zero"?

"Sets with Mass Zero" refer to a concept in mathematics where the sum of the elements in a set equals zero. This means that all the elements in the set have a value of zero or are negative and positive values that cancel each other out.

Why are "Sets with Mass Zero" considered mysterious?

These sets are considered mysterious because they challenge our understanding of traditional mathematics. In most cases, we are used to sets having a non-zero sum, so the idea of a set with a mass of zero seems counterintuitive and intriguing.

Are there real-life applications for "Sets with Mass Zero"?

Yes, the concept of "Sets with Mass Zero" can be applied in various fields such as physics, engineering, and economics. For example, in physics, the idea of balancing forces to achieve a net force of zero can be represented using "Sets with Mass Zero".

How can "Sets with Mass Zero" be explored?

Exploring "Sets with Mass Zero" can involve mathematical calculations and proofs to understand the concept. It can also involve visual representations, such as graphing and diagrams, to visualize the concept and its applications.

What are the implications of "Sets with Mass Zero" in the field of mathematics?

The concept of "Sets with Mass Zero" challenges our understanding of traditional mathematics and can lead to the development of new theories and concepts. It also highlights the importance of considering all possibilities and not limiting our thinking to what is conventionally accepted.

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