In probability theory, if the probability density f (x) of continuous random variable changes the value of finite points of F (x), f (x) is still the probability density. Why?

Probability is equal to the integral value of probability density. From the knowledge of definite integral, we can know that changing the value of individual points does not affect the definite integral. For example, for an area, removing one line or several lines will not affect the size of the area

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