Measure theory books emphasising on the approximation of a measurable function by a sequence of simple and step functions.

Measure theory books emphasising on the approximation of a measurable function by a sequence of simple and step functions.

I am a beginner of measure theory After studying the measurable function from Stein Shakarchis book I find some approximation theorems of measurable functions by simple and step functions I have read them all But still I am struggling in it What is the way of approximating a function by a sequence ofsimple and step functions is still unknown to me I also dont find any online resource which elaborates this fact nicely by demonstrating some useful examples So can anybody suggest which has nice explanation about this area and also whichor is available online Then it will be really helpful for me Thank you very much

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