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Jyan

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I'm working on some MIT OCW for probability theory, and I've come across some confusing notation in the assignmnet. Look at exercise 3 here:

http://ocw.mit.edu/courses/electric...y-fall-2008/assignments/MIT6_436JF08_hw01.pdf

I understand what the max and min functions do on their own (find the max or min value of the function subject to the constraints written under the function), but what does it mean when they are combined like this?

Are they applied one after the other? So that max min f(x,y) would mean to find the minimum function f(x) (whatever that means, there is no given measure of the "size" of a function) then find the maximum value of the function f(x). Or are they somehow applied together?

Perhaps [tex]min_{y \in B} f(x,y)[/tex] means to find the function f(x) (set y constant) such that f(x) has the smallest minimum value (the global min)? likewise, [tex]max_{x\in B} f(x,y)[/tex] means to find the function f(y) (set x constant) such that f(y) has the largest maximum value (the global max)? I don't think this is right though, since it is easy to imagine a counter example for the statement we are supposed to prove.

Anyone know exactly what this notation means?

Thanks for any help.

http://ocw.mit.edu/courses/electric...y-fall-2008/assignments/MIT6_436JF08_hw01.pdf

I understand what the max and min functions do on their own (find the max or min value of the function subject to the constraints written under the function), but what does it mean when they are combined like this?

Are they applied one after the other? So that max min f(x,y) would mean to find the minimum function f(x) (whatever that means, there is no given measure of the "size" of a function) then find the maximum value of the function f(x). Or are they somehow applied together?

Perhaps [tex]min_{y \in B} f(x,y)[/tex] means to find the function f(x) (set y constant) such that f(x) has the smallest minimum value (the global min)? likewise, [tex]max_{x\in B} f(x,y)[/tex] means to find the function f(y) (set x constant) such that f(y) has the largest maximum value (the global max)? I don't think this is right though, since it is easy to imagine a counter example for the statement we are supposed to prove.

Anyone know exactly what this notation means?

Thanks for any help.

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