Affine space/Point set/Barycentric combination/Point/Fact

For a family ${\displaystyle {}P_{i}}$, ${\displaystyle {}i\in I}$, of points in an affine space ${\displaystyle {}E}$, a barycentric combination

${\displaystyle \sum _{i\in I}a_{i}P_{i}}$

defines a unique point in ${\displaystyle {}E}$.