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calvo.md and calvo_machine_learn.md: $L^2$ definition removed but notation still used #328

@mmcky

Description

@mmcky

Summary

PR #312 ("[amss] Update Tom's edits to AMSS and Calvo Lectures") removed the local definition of square-summable / $L^2$ from the three Calvo lectures, but several places still use the $L^2$ notation without a definition, leaving readers without context for what space is being referenced.

Locations still using L^2 after the definition was removed

lectures/calvo.md — 7 occurrences

Line Context
330 $\vec \mu =\{\mu_t\}_{t=0}^\infty \in L^2$ into an inflation sequence
331 $\vec \theta = \{\theta_t\}_{t=0}^\infty \in L^2$.
334 $\vec v = \{v_t\}_{t=0}^\infty \in L^2$ that satisfies
340 sequence $\vec \mu \in L^2$.
342 At this point $\vec \mu \in L^2$ is an arbitrary exogenous policy.
453 $\{x_{t+1}, \mu_t \}_{t=0}^\infty$ sequences, with each sequence belonging to $L^2$:
460 where we require that $\{x_{t+1}, \mu_t \}_{t=0}^\infty \in L^2 \times L^2 .$

lectures/calvo_machine_learn.md — 1 occurrence

Line Context
208 \vec \theta \in L^2

lectures/calvo_abreu.md — clean

calvo_abreu.md had the same definition removed and no remaining $L^2$ references, so it's consistent.

Why it matters

Earlier in each affected lecture, the assumption on $\vec\mu$ was weakened from "square-summable" to "bounded" (a reasonable simplification — the discounted geometric structure of the forward solution is well-defined under boundedness). But the later sections that still use $L^2$ now reference an undefined space. A reader going top-to-bottom encounters $\vec\mu \in L^2$ at line 330+ in calvo.md with no prior definition or external pointer.

Suggested fix

Either:

  1. Reintroduce a brief $L^2$ definition in each of the two affected lectures (could be a one-liner: "$L^2$ denotes the space of square-summable sequences"), or
  2. Replace the remaining $L^2$ references with the weaker "bounded" framing if that's now the intended assumption end-to-end, or
  3. Cross-link to a single canonical definition in one of these lectures and have the others reference it.

Context

Surfaced by GitHub Copilot's PR review during sync of these lectures into lecture-dp (QuantEcon/lecture-dp#11). The PR is byte-identical to this repo's current main, so this issue belongs upstream.

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