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Question on notation of random variables in probability ensembles

Let’s consider this definition of computational indistinguishability. Computational indistinguishability. A probability ensemble $X={X(a, n)}_{a in{0,1}^{*} ; n in mathbb{N}}$ is an infinite sequence of random variables indexed by $a in{0,1}^{*}$ and $n in mathbb{N}$. In the context of secure computation, the value $a$ will represent the parties’ inputs and $n$ will represent the security parameter.::Listen

Let’s consider this definition of computational indistinguishability.

Computational indistinguishability. A probability ensemble $X={X(a, n)}_{a in{0,1}^{*} ; n in mathbb{N}}$ is an infinite sequence of random variables indexed by $a in{0,1}^{*}$ and $n in mathbb{N}$. In the context of secure computation, the value $a$ will represent the parties’ inputs and $n$ will represent the security parameter. Two probability ensembles $X={X(a, n)}_{a in{0,1}^{*} ; n in mathbb{N}}$ and $Y={Y(a, n)}_{a in{0,1}^{*} ; n in mathbb{N}}$ are said to be computationally indistinguishable, denoted by $X stackrel{c}{equiv} Y$, if for every non-uniform polynomial-time algorithm $D$ there exists a negligible function $mu(cdot)$ such that for every $a in{0,1}^{*}$ and every $n in mathbb{N}$,
$$
|operatorname{Pr}[D(X(a, n))=1]-operatorname{Pr}[D(Y(a, n))=1]| leq mu(n)
$$

From my understanding $D$ is the distinguishing algorithm, e.g. the adversary in security proofs. An instance of the random variable $X(a,n)$ is considered as the encryption algorithm. However from my understanding only the output of the encryption algorithm, e.g. the ciphertext, is passed to $D$. For people coming from mathematical background this is a bit confusing because random variable is a function $X:Ω rightarrow Ε$ where $Ω$ is the σ-algebra of the events space and $E$ is a measurable space.

Can someone help me clarify the notation and the definition that is used?
Thanks in advance.

Breaking: Terra blockchain officially halted following LUNA price collapse

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