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.
You are referring to Euler's number. It is pronounced like "eh-uh-le-uh" because the name is German. Euler's number is the number e, which is the base of the natural logarithm. The number e is extremely prominent in any mathematical endeavour involving calculus in any way, as it has many useful properties. For example, the derivative of the function f(x) = e^x is the function df(x) = e^x = f(x). It is the only function that has this property. The natural logarithm is itself also very useful. It was discovered by studying properties of the integral of the function f(x) = 1/x, which did not have any closed form antiderivative in terms of the elementary functions of that time period, even though g(x) = x^n had the simple antiderivative Ig(x, C) = (x^(n+1))/(n+1) + C for any real n except n = -1. It was eventually discovered that the function f(x) defined as the definite integral of f(t) = 1/t from t = 1 to t=x had the properties of a logarithmic function with base e. e is transcendental, so it is both irrational and is not the root of any polynomial function with rational coefficients. Or in simple words 2.718281828459
Characteristic function of any borel set is an example of simple Borel function
You could describe any measurable characteristic as a trait.
any measurable quantity
The function of simple columnar tissue is to provide protection against any bacteria that might be ingested. However, it is still permeable enough for necessary ions to enter.KKK
No, not in any measurable number.
he has not in any significant measurable way
The moon does not have any measurable atmosphere.
a measurable trait in which there is some evidence of the operation of a simple major cause, but in which the variation within the putative categories is such as to cause overlap and hence ambiguity in classification of any particular reading.
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.
To get a hard copy output of any soft print in the screen in a form of a paper! Simple..
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.