Yes. For every measurable function, f there's a sequence of simple functions Fn that converge to f m-a.e (wich means for each e>0, there's X' such that Fn|x' -->f|x' and m(X\X')<e).
If X has any discrete probability distribution then the sum of a number of observations for X will be normal.
The "zero" or "root" of such a function - or of any other function - is the answer to the question: "What value must the variable 'x' have, to let the function have a value of zero?" Or any other variable, depending how the function is defined.
The function is a simple linear function and so its nature does not limit the domain or range in any way. So the domain and range can be the whole of the real numbers. If the domain is a proper subset of that then the range must be defined accordingly. Similarly, if the range is known then the appropriate domain needs to be defined.
False. You can only replace it with a number from the domain of the function.
The function is not defined at any values at which the denominator is zero.
One example of a simple Borel measurable function is the indicator function of a Borel set. This function takes the value 1 on the set and 0 outside the set, making it easy to determine its measurability with respect to the Borel sigma algebra.
You could describe any measurable characteristic as a trait.
any measurable quantity
The moon does not have any measurable atmosphere.
he has not in any significant measurable way
No, not in any measurable number.
To get a hard copy output of any soft print in the screen in a form of a paper! Simple..
The word "measurable" is a hedge. This means "There is no influence, none whatsoever, and when I say that I mean that if there is any influence we can't measure it, not with the equipment we now have." That last bit, which is what the word "measurable" is there for, is there to protect the speaker in case he is wrong.
Any two dimentional geometric figure has a measurable length. This measurement is called circumference. This is also called a plane figure. Examples of plane figures with measurable lengths are: triangle, square, circle, and rectangle.
You can, but it wouldn't bring you any measurable advantage.
Data is arranged logically according to size or time of occurrence or some other measurable or non measurable characteristics...
If X has any discrete probability distribution then the sum of a number of observations for X will be normal.