\begin{definition}[Definition:Integral Transform]
Let $p$ be a variable whose domain is a subset of the set of real numbers $\R$.
Let $\closedint a b$ be a closed real interval for some $a, b \in \R: a \le b$.
Let $f: \closedint a b \to \R$ be a real function defined on the domain $\closedint a b$.
Let $\map K {p, x}$ be a real-valued function defined for all $p$ in its domain and all $x \in \closedint a b$.
Let $\map f x \map K {p, x}$ be integrable {{WRT|Integration}} $x$ for all $p$ in its domain and all $x \in \closedint a b$.
Consider the real function $\map F p$ defined as:
:$\map F p = \ds \int_a^b \map f x \map K {p, x} \rd x$
Then $\map F p$ is an '''integral transform''' of $\map f x$.
\end{definition}