measurable functions

Are Continuous Functions Borel Measurable?

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Are Continuous Functions Borel Measurable? In particular, every continuous function between topological spaces that are equipped with their Borel σ-algebras is measurable. Is uniformly continuous function measurable? A uniform space is called ^”measurable if the pointwise limit of any sequence of uniformly continuous functions (real valued) is uniformly continuous. A uniform space is called measurable

Are All Continuous Functions Measurable?

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Are All Continuous Functions Measurable? Are all continuous functions measurable? Lebesgue measure Are all continuous functions Borel measurable? Continuous functions are not always measurable. It depends on the σ-algebra! Actually, continuous functions are measurable for an algebra F if and only if F contains the Borel algebra. How do you prove a continuous function is