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content/Definitions/Terminology/Pointwise.md
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content/Definitions/Terminology/Pointwise.md
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# Definition
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$X$, $M$ then $f : X \to \mathbb{C}$ [[Measure|measure]] form an algebra under **pointwise** operations:
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$$(f + g)(x) = f(x) + g(x)$$
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$$(f \circ g)(x) = f(x) \times g(x)$$
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# Example
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$(f+g)(x) = f(x) + g(x)$
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The plus part of this operation is the pointwise part
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