distribution.
a continuous functional on a space of test functions (Schwartz space), which generalizes the concept of locally integrable functions
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About distribution
In mathematical analysis, distributions are a type of generalized function that makes it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. Distributions are widely used in the theory of partial differential equations, where it may be easier to establish the existence of distributional solutions than classical solutions, or appropriate classical solutions may not exist. Distributions are also important in physics and engineering where many problems naturally lead to differential equations whose solutions or initial conditions are distributions, such as the Dirac delta function.
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