set of points of the index set determine the properties of the stochastic process. Any stochastic process with a countable index set already meets the separability conditions, so discrete-time stochastic processes are always separable. A theorem by Doob, sometimes known as Doob's separability theorem, says that any real-valued continuous-time stochastic process has a separable modification. Versions of this theorem also exist for more general stochastic processes with index sets and state spaces other than the real line. Independence Two stochastic processes and defined on the same probability space with the same index set are said be independent if for all and for every choice of epochs , the random vectors and are independent. Uncorrelatedness Two stochastic processes and are called uncorrelated if their cross-covariance is zero for all times. Formally: . Independence implies uncorrelatedness If two stochastic processes and are independent, then they are also uncorrelated. Orthogonality Two stochastic processes and are called orthogonal if their cross-correlation is zero for all times. Formally: . Skorokhod space A Skorokhod space, also written as Skorohod space, is a mathematical space of all the functions that are right-continuous with left limits, defined on some interval of the real line such as or , and take values on the real line or on some metric space. Such functions are known as càdlàg or cadlag functions, based on the acronym of the French phrase continue à droite, limite à gauche. A Skorokhod function space, introduced by Anatoliy Skorokhod, is often denoted with the letter , so the function space is also referred to as space . The notation of this function space can also include the interval on which all the càdlàg functions are defined, so, for example, denotes the space of càdlàg functions defined on the unit interval . Skorokhod function spaces are frequently used in the theory of stochastic processes because it often assumed that the sample functions of continuous-time stochastic processes belong to a Skorokhod space. Such spaces contain continuous functions, which correspond to sample functions of the Wiener process. But the space also has functions with discontinuities, which means that the sample functions of stochastic processes with jumps, such as the Poisson process (on the real line), are also members of this space. Regularity In the context of mathematical construction of stochastic processes, the term regularity is used when discussing and assuming certain conditions for a stochastic process to resolve possible