 Conversely, the values of the distribution "Tf" on test functions in D(R) determine the pointwise almost everywhere values of the function "f" on R. In a conventional abuse of notation, "f" is often used to represent both the original function "f" and the corresponding distribution "Tf".This example suggests the definition of a distribution as a linear and, in an appropriate sense, continuous functional on the space of test functions D(R).Similarly, if μ is a Radon measure on R, then a corresponding distribution "R"μ may be defined by

This integral also depends linearly and continuously on formula_1, so that "R"μ is a distribution.