- #1

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Every ##f_i## is the limit (almost everywhere) of "step" functions, that is a linear combination of rectangles indicator functions.

Is there a way to prove that also ##f## is the limit of "step" functions?

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- Thread starter Unconscious
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- #1

- 74

- 12

Every ##f_i## is the limit (almost everywhere) of "step" functions, that is a linear combination of rectangles indicator functions.

Is there a way to prove that also ##f## is the limit of "step" functions?

- #2

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- #3

Science Advisor

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In what sense? You certainly will have [itex]\int \vert f-f_{n} \vert \rightarrow 0 [/itex] but I think you will have problems with other metrics .Is there a way to prove that also is the limit of "step" functions?

- #4

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I mean pointwise convergence, optionally except on a measure-zero set of ##\mathbb{R}^n##.

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