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  1. #1
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    measure theory

    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.
    Time independence: [∂E(g)]˛=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c˛

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    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.

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    Quote Originally Posted by hanzoganz
    Lebesgue thoery is indeed a beautiful theory
    Is it needed to fully understand the theory of probability?
    Time independence: [∂E(g)]˛=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c˛

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    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

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    perturbation theory

    Quote Originally Posted by hanzoganz
    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.
    Time independence: [∂E(g)]˛=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c˛

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    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.

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    general form

    Quote Originally Posted by hanzoganz
    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.
    Time independence: [∂E(g)]˛=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c˛

 

 

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