# Questions tagged [simple-functions]

Use this tag for questions related to simple functions

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### Simplification of sum of exponentials? [closed]

Is there a way to simplify the expression $\sum _{k=0}^n 2^k$? That is, is there a way to write it without a $\sum$ or $\prod$ operator?
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### Representation of the sum of simple functions

In the book Elementary Introduction to the Lebesgue Integral by Steven Krantz, the author considers two simple functions $\varphi$ and $\psi$ and says that the sum of these two functions has the ...
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### Properties of Simple Functions

Suppose $f$ is a non-negative measurable function. i.e $f \in L^+$. Is it true that f is the decreasing limit of a sequence of simple functions? I'm suspecting that it's false, since it's we don't ...
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### Horizontal truncation of the upper signed Lebesgue integral

Prove or disprove that $\forall d\ge_\mathbb Z0,\forall f\colon\mathbb R^d\to[0,+\infty],$ \lim_{n\to+\infty}\overline{\int_{\mathbb R^d}}\min(f(x),n)\,\mathrm{d}x=\overline{\int_{\mathbb R^d}}f(x)\,...
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### Deterministic algorithm with math

Well, I’m not too good with math and I don’t know all of the special symbols, but I have one (maybe) simple goal to achieve: How do I create a deterministic algorithm in math? Well, the only input ...
This is me being extremely stupid, but a parabola with a vertex $(2,6)$ and $x$-intercepts of $(-4,0),(8,0)$ can be described with the equation $y=\frac{-(x+4)(x-8)}{6}$(my answer) which would also be ...
Suppose the step function is defined as follows. A function $f$ is a step function on $[a,b]$, if there exists a finite partition $P$ of $[a,b]$ such that $f$ is constant on the interior of each ...