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# Questions tagged [simple-functions]

Use this tag for questions related to simple functions

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### A question on the integral of nonnegative functions using the integral of simple functions

Question: In Folland's Real Analysis, on page $50$, he says, when discussing the integral of simple functions, that we can extend the integral of a simple function to all nonnegative functions $f$ by ...
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### L2 convergence for a simple function approximation

Consider the problem on the picture. I am struggling with part (b) of the excercise. I have managed to show that we have $L^1$ convergence, but I am unable to show $L^2$ convergence. Does anyone have ...
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### Proof clarification measure given by integral

While studying measure theory, I encountered a simple proposition which contains a step I was not able to follow. First, here are some relevant definitions(not all of them, since there would be too ...
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### Multiplication of simple function looks like?

I was wondering what does the multiplication of two Lebesgue integrable simple functions look like. Assume integral of a function f is defined as
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### How to deal with nonmeasurable sets when proving simple function is measurable?

I know the simple function f is defined as ai if x is in a sequence of measurable set Ei, 0 if it is not in the union of Ei. I tried to prove that simple function is measurable. It is measurable ...
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### what does it mean by $\# \{ i : x_i \le t \}$?
I was reading through some manuscript and wanted to try to implement some stuff mentioned in the text. I came across this equation equation $= \# \{ i : x(i) \le t \}$ I went through a couple of ...