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The R-value is the building industry term [3] for thermal resistance "per unit area." [4] It is sometimes denoted RSI-value if the SI units are used. [5] An R-value can be given for a material (e.g., for polyethylene foam), or for an assembly of materials (e.g., a wall or a window). In the case of materials, it is often expressed in terms of R ...
In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to ...
An arbitrary function φ : R n → C is the characteristic function of some random variable if and only if φ is positive definite, continuous at the origin, and if φ(0) = 1. Khinchine’s criterion. A complex-valued, absolutely continuous function φ, with φ(0) = 1, is a characteristic function if and only if it admits the representation
An everywhere differentiable function g : R → R is Lipschitz continuous (with K = sup |g′(x)|) if and only if it has a bounded first derivative; one direction follows from the mean value theorem. In particular, any continuously differentiable function is locally Lipschitz, as continuous functions are locally bounded so its gradient is ...
Every (globally) Lipschitz-continuous function is absolutely continuous. [6] If f: [a,b] → R is absolutely continuous, then it is of bounded variation on [a,b]. [7] If f: [a,b] → R is absolutely continuous, then it can be written as the difference of two monotonic nondecreasing absolutely continuous functions on [a,b].
The extreme value theorem states that for any real continuous function on a compact space its global maximum and minimum exist. The concept of metric space itself is defined with a real-valued function of two variables, the metric, which is continuous. The space of continuous functions on a compact Hausdorff space has a particular importance.
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
A continuous variable is a variable such that there are possible values between any two values. For example, a variable over a non-empty range of the real numbers is continuous, if it can take on any value in that range. [4]