Step Function vs Simple Function

I think everything is fine , Step function is just a special case of simple function with the sets in simple function taken to be just intervals, You can also conclude that every Step function is a Simple function but Converse is not true.


You have a good explanation in the following link: https://mathcs.org/analysis/reals/integ/answers/simpfun1.html

Tags:

Real Analysis

Measure Theory

Related

How to evaluate the sum $\sum_{n=1}^{\infty}\frac{1}{(2n+1)(2n+2)}\left(1+\frac{1}{2}+...+\frac{1}{n}\right)$ In which spaces can one "flip" the topology? Primality testing for 64 bit numbers If $P(A) \neq 0$ and $P(B) \neq 0$, then $P(B|A) \geq P(B)$ is equivalent to $P(A|B) \geq P(A)$ Is there an intuitive way of visualising complex roots? Find $x\in \Bbb R,$ solving $x=\sqrt{1+\sqrt{1+\sqrt{1+x}}}$ Alternative definition for tensor product which nowhere occurs (to my knowledge) Prove that there exists two consecutive natural numbers such that sum of all digits of each number is multiple of $2017$. How do you graph a negative number raised to $x$? Convergence in probability does not imply almost sure convergence? Subfields of a cyclotomic field If and when a linear system has exactly three solutions

Recent Posts