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f+ and f-

What do these mean? If it helps it's in the context of lebesgue integration. I can't find a definition in my notes or online anywhere.
(edited 10 years ago)
Original post by james22
What do these mean? If it helps it's in the context of lebesgue integration. I can't find a definition in my notes or online anywhere.


Accordig to S.J Taylor's Introduction to Measure and Integration

f+(x)=max⁡[0,f(x)]f_+(x)=\max[0,f(x)]

f−(x)=−min⁡[0,f(x)]f_-(x)=-\min[0,f(x)]

Is that the usage you're refering to?
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james22
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Original post by ghostwalker
Accordig to S.J Taylor's Introduction to Measure and Integration

f+(x)=max⁡[0,f(x)]f_+(x)=\max[0,f(x)]

f−(x)=−min⁡[0,f(x)]f_-(x)=-\min[0,f(x)]

Is that the usage you're refering to?


Thanks, but I don't think that works. One of the properties is that |f|=(f+)+(f-).
Original post by james22
Thanks, but I don't think that works. One of the properties is that |f|=(f+)+(f-).


That property is consistent with that definition.

You might like to recheck.
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james22
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Original post by ghostwalker
That property is consistent with that definition.

You might like to recheck.


Ah yes, I missread what you wrote. I thought that you were refering to the supremum of an interval rather than the maximum of a set.
Original post by james22
Ah yes, I missread what you wrote. I thought that you were refering to the supremum of an interval rather than the maximum of a set.


I used the book's symbolism. I think the [,] is bracketing the arguments of the max/min functions.

Anyhow, glad it made sense.

Key point the book makes is that f+ and f- are non-negative.
(edited 9 years ago)

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