A Lebesgue point of a locally integrable function 
on 
is a point 
at which there is a finite value
satisfying
 |
Here 
is an open ball and 
is its Lebesgue measure.
The value 
is uniquely determined and is unchanged by altering 
on a set of measure
zero. Almost every point is a Lebesgue point, and 
almost
everywhere (Stein 1993). For a continuous
function, every point is a Lebesgue point with 
. This representative makes
precise the initial values in the Schrödinger
pointwise convergence problem.
