What is the meaning of 'continuous almost everywhere - alpha'?

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The term "continuous almost everywhere - alpha" refers to a function that is continuous on a measurable space except for a subset A, where the measure of A is zero according to the measure alpha. This indicates that the continuity property holds for almost all points in the space, with the exception of a negligible set. The discussion emphasizes the importance of specifying the measure in use, as it clarifies the context of "almost everywhere." Understanding this concept is crucial for analyzing functions in measure theory and real analysis.

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what does continuous almost everywhere - alpha means?

I know that the term almost everywhere means that the property holds everywhere on the measurable space except on a subset of measure 0,what I don't really understand is the term almost everywhere-alpha.
 
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It's hard to say what that's intended to mean without knowing more context, but people will often indicate the specific measure that "almost everywhere" refers to, if it's not obvious from context.
 
yes, I think you're right, the measure which is used here is alpha and the function is probably continuous everywhere except on a subset A of the measurable space of measure alpha(A)=0
 

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