here are the properties of the joint density function, can someone explain me the 4° point? (it says: for every... as a point of continuity of f)

here are the properties of the joint density function, can someone explain me the 4° point? (it says: for every... as a point of continuity of f)

In a simpler one-dimension case, we have: $$ f(x)=\frac{dF(x)}{dx} $$ and in the contrary, the integral: $$ F(x)=\int_{-\infty}^x f(x)dx $$ We call $f(x)$ the probability density function(PDF), and $F(x)$ the cumulative density function(CDF). $f(x)$ denotes the probability density on the point x, $F(x)$ denotes the integral of probability density from $-\infty$ to the point x.