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In the continuous case, \(f\) would vary continuously on \(S\) and we might have a differential equation specifying how \(f\) varies.
From Eqs. (B.2), (B.6) and (B.7), the discrete form retains continuity and coercivity yielding a unique solution as in the continuous case.
In the continuous case, the counterpart of the probability mass function is the probability density function, also denoted by f(x).
In the discrete case the weights are given by the probability mass function, and in the continuous case the weights are given by the probability density function.
Corollary 2.3 (Continuous case).
In the continuous case:.
Let T = ℝ, i.e., the continuous case.
Figure 2 Venn's diagram: continuous case.
In the continuous case: (mu(t)equiv0).
(i) or any any closed interval (the continuous case), and.
Our second basic motivation comes from the continuous case.
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