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 Post subject: An unknown signPosted: Wed, 12 Oct 2011 17:51:49 UTC

Joined: Sat, 8 Oct 2011 17:57:59 UTC
Posts: 5
Hello,

Inside two measure spaces: (X, sigmaAlgebraA, b), (Y, sigmaAlgebraB, v)
Suppose you have a function u : X x Y -> [0,infinity]

What does the following mean in this setting?

x |-> u(x, y)

or

x |-> Integral ( u(x, y)v(dy)

I dont understand the meaning of the symbol '|->'. Tried to google it several times with no luck.

In Latex its called /mapsto.

Thank you for you help.

Henrik Løv

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 Post subject: Re: An unknown signPosted: Wed, 12 Oct 2011 19:38:55 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12102
Location: Austin, TX
henrikloev wrote:
Hello,

Inside two measure spaces: (X, sigmaAlgebraA, b), (Y, sigmaAlgebraB, v)
Suppose you have a function u : X x Y -> [0,infinity]

What does the following mean in this setting?

x |-> u(x, y)

or

x |-> Integral ( u(x, y)v(dy)

I dont understand the meaning of the symbol '|->'. Tried to google it several times with no luck.

In Latex its called /mapsto.

Thank you for you help.

Henrik Løv

It means you have a function which takes x and gives you the function .

Basically the notation means you're defining the function by telling you what the image of a point is.

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 Post subject: Re: An unknown signPosted: Wed, 12 Oct 2011 22:38:12 UTC

Joined: Sat, 8 Oct 2011 17:57:59 UTC
Posts: 5

So,

= ?

I dont fully understand what you mean by

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 Post subject: Re: An unknown signPosted: Wed, 12 Oct 2011 23:21:55 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12102
Location: Austin, TX
henrikloev wrote:

So,

= ?

I dont fully understand what you mean by

is a function from which takes the value at .

I don't know what your is btw, so I have no comment on that bit.

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 Post subject: Re: An unknown signPosted: Thu, 13 Oct 2011 12:11:48 UTC

Joined: Sat, 8 Oct 2011 17:57:59 UTC
Posts: 5
Suppose .

What would then be?

I don't understand, because and the function you write is ?

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 Post subject: Re: An unknown signPosted: Thu, 13 Oct 2011 14:23:42 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6007
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
henrikloev wrote:
Suppose .

What would then be?

I don't understand, because and the function you write is ?

In this case, would just be the function that takes every x and add y to it.

It is just a notation. is the function , or if you prefer the lambda-calculus notation, . Of course, this notation doesn't tell you the domain or the codomain of the function, which needed to be specified elsewhere, e.g. .

Back to --- it is the function that takes whatever x you input, and spits out the value , i.e. the function that takes x in X as input, and output the integral of the nonnegative (measurable) function with respect to measure on Y. Note the two different types of arrows here --- is used for specifying the domain/codomain, and is used for specifying the value of the function at (generic) argument.

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 Post subject: Re: An unknown signPosted: Thu, 13 Oct 2011 17:39:02 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12102
Location: Austin, TX
outermeasure wrote:
henrikloev wrote:
Suppose .

What would then be?

I don't understand, because and the function you write is ?

In this case, would just be the function that takes every x and add y to it.

It is just a notation. is the function , or if you prefer the lambda-calculus notation, . Of course, this notation doesn't tell you the domain or the codomain of the function, which needed to be specified elsewhere, e.g. .

Back to --- it is the function that takes whatever x you input, and spits out the value , i.e. the function that takes x in X as input, and output the integral of the nonnegative (measurable) function with respect to measure on Y. Note the two different types of arrows here --- is used for specifying the domain/codomain, and is used for specifying the value of the function at (generic) argument.

I don't know, I interpreted his question as assigning x to the translation by x operator on , since he said was a function. I agree that does what you said, but we're talking about the assignment .

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