This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations.(January 2023) (Learn how and when to remove this message)
Function that attains finitely many values
In the mathematical field of real analysis, a simple function is a real (or complex)-valued function over a subset of the real line, similar to a step function. Simple functions are sufficiently "nice" that using them makes mathematical reasoning, theory, and proof easier. For example, simple functions attain only a finite number of values. Some authors also require simple functions to be measurable; as used in practice, they invariably are.
A basic example of a simple function is the floor function over the half-open interval [1, 9), whose only values are {1, 2, 3, 4, 5, 6, 7, 8}. A more advanced example is the Dirichlet function over the real line, which takes the value 1 if x is rational and 0 otherwise. (Thus the "simple" of "simple function" has a technical meaning somewhat at odds with common language.) All step functions are simple.
Simple functions are used as a first stage in the development of theories of integration, such as the Lebesgue integral, because it is easy to define integration for a simple function and also it is straightforward to approximate more general functions by sequences of simple functions.
analysis, a simplefunction is a real (or complex)-valued function over a subset of the real line, similar to a step function. Simplefunctions are sufficiently...
under the simplefunction. In this way, the partitioning of the range of f implies a partitioning of its domain. The integral of a simplefunction is found...
function for an intermediate value of the independent variable. A closely related problem is the approximation of a complicated function by a simple function...
the same syntax as a function call. Functors are more powerful than simplefunction pointers, being able to contain their own data values, and allowing...
The SimpleFunction Point (SFP) method is a lightweight Functional Measurement Method. The SimpleFunction Point method was designed by Roberto Meli in...
the function has simple poles.[clarification needed] The gamma function has no zeros, so the reciprocal gamma function 1/Γ(z) is an entire function. In...
pulse generators are primarily used for working with digital circuits. Simplefunction generators usually generate triangular waveform whose frequency can...
Look up simple in Wiktionary, the free dictionary. Simple or SIMPLE may refer to: Simplicity, the state or quality of being simpleSimple (album), by...
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all...
function of two independent variables. Such a function requires only three parameters (the intercept and two slopes). Replacing this simplefunction with...
The Function Block Diagram (FBD) is a graphical language for programmable logic controller design, that can describe the function between input variables...
which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known...
definition of Lebesgue integral to functions that take values in a Banach space, as the limit of integrals of simplefunctions. Let ( X , Σ , μ ) {\displaystyle...
of simplefunctions. The case of Type II geometric integrals reduces to exactly the case of classical Lebesgue integration. Because simplefunctions generalize...
everywhere. Any simplefunction is a finite linear combination of indicator functions. By linearity the above property holds for simplefunctions: if X n {\displaystyle...
meromorphic in the whole complex plane, and has a simple pole at every non-positive integer. The Riemann zeta function is also meromorphic in the whole complex...
location-scale family, its quantile function for arbitrary parameters can be derived from a simple transformation of the quantile function of the standard normal distribution...
metric based on twelve primitive (simple) counts that affect or show Bang, defined as "the measure of true function to be delivered as perceived by the...
In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether...
cases, a relatively simplefunction does not have integrals that can be expressed in closed form involving only elementary functions, include rational and...
mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value...
a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. In simple terms, a convex function graph...
Global Information