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The product of a step function with a number is also a step function. As such, the step functions form an algebra over the real numbers. A step function takes only a finite number of values. If the intervals , for =,, …, in the above definition of the step function are disjoint and their union is the real line, then () = for all .
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A function f : [a, b] → R is called a regulated function if it is the uniform limit of a sequence of step functions on [a, b]: there is a sequence of step functions (φ n) n∈N such that || φ n − f || ∞ → 0 as n → ∞; or, equivalently, for all ε > 0, there exists a step function φ ε such that || φ ε − f || ∞ < ε; or ...
Then f is a non-decreasing function on [a, b], which is continuous except for jump discontinuities at x n for n ≥ 1. In the case of finitely many jump discontinuities, f is a step function. The examples above are generalised step functions; they are very special cases of what are called jump functions or saltus-functions. [8] [9]
Event management is the application of project management to the creation and development of small and/or large-scale personal or corporate events such as festivals, conferences, ceremonies, weddings, formal parties, concerts, or conventions.
The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Different conventions concerning the value H(0) are in use.