measure theory

[AntonioLao]

Information about the theory of measure can be viewed at these links http://en.wikipedia.org/wiki/Measure_theory and http://mathworld.wolfram.com/MeasureTheory.html and http://www.maths.bris.ac.uk/~maval/an3.html and http://www.math.niu.edu/~rusin/known-math/index/28-XX.html and http://www.math.uconn.edu/~bass/lecture.html and http://www.probability.net/
These are resources that describe what measure theory is using mathematics. That it has more to do with probability and the true meaning of 1/∞ than it has to do with absolute 0.

[hanzoganz]

Lebesgue thoery is indeed a beautiful theory, altough i have to say I haven't used it that much as to be able to express my toughts about it. I guess time will tell.

[AntonioLao]

Lebesgue thoery is indeed a beautiful theory

Is it needed to fully understand the theory of probability?

[hanzoganz]

I guess probability nowadays can be defined from diferent perspectives. I don't work on probability, altough i use a bit of stochastic processes, i.e., inserting some aleatory perturbations to functions.
So, if you want to study events with perturbations that are not easily measurable, from the classical point of view, i.e., high dimensions, for example, you will need it.
So, it depends what you want to study and from there you choose your tools. Same as in any other trade.
Cheers

[AntonioLao]

if you want to study events with perturbations that are not easily measurable

Such that a * b = a - b ? I'm working on something along this kind of dimensional violations of math which I called dysfunctional analysis.

[hanzoganz]

That operation you are defining can be tought as inserted in Group Theory. It is pefectly valid if it has the 4 -or 5 for abelian- properties of a group. It is a fun excercise to invent your binary operations and check that they have the properties of a group.

[AntonioLao]

It is a fun excercise to invent your binary operations and check that they have the properties of a group.

I did the graphs in nth power polar form and the higher the degree the curves seem to move away from the unit circle.