Learning.Environment.instIsMarkovKernelProdν0
Instance
No docstring.
Types
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𝓞 : Type u_1m𝓞 : MeasurableSpace 𝓞A measurable space is a space equipped with a σ-algebra. -
𝓐 : Type u_2m𝓐 : MeasurableSpace 𝓐 -
𝓨 : Type u_3m𝓨 : MeasurableSpace 𝓨
Given
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env : Environment 𝓞 𝓐 𝓨A stochastic environment.
Then
ProbabilityTheory.IsMarkovKernel env.ν0MeasurableSpace : Type u_6 → Type u_6A measurable space is a space equipped with a σ-algebra.
Learning.Environment : (𝓞 : Type u_5) →
(𝓐 : Type u_6) →
(𝓨 : Type u_7) → [MeasurableSpace 𝓞] → [MeasurableSpace 𝓐] → [MeasurableSpace 𝓨] → Type (max (max u_5 u_6) u_7)A stochastic environment. At each round, an observation is drawn prior to the algorithm taking an action. Then the environment provides feedback based on the observation and the action.Go to its page
ProbabilityTheory.IsMarkovKernel : {α : Type u_1} →
{β : Type u_2} → {mα : MeasurableSpace α} → {mβ : MeasurableSpace β} → ProbabilityTheory.Kernel α β → PropA kernel is a Markov kernel if every measure in its image is a probability measure.
Learning.Environment.ν0 : {𝓞 : Type u_1} →
{𝓐 : Type u_2} →
{𝓨 : Type u_3} →
{m𝓞 : MeasurableSpace 𝓞} →
{m𝓐 : MeasurableSpace 𝓐} →
{m𝓨 : MeasurableSpace 𝓨} → Learning.Environment 𝓞 𝓐 𝓨 → ProbabilityTheory.Kernel (𝓞 × 𝓐) 𝓨Distribution of the first feedback given the first observation and action: the feedback kernel at time `0` applied to the empty history.Go to its page
Code
deriving IsMarkovKernel
Proof
deriving IsMarkovKernel
Meaning last changed in v4.34.0-rc2-76-g565f652 (2026-09-10).
Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file · open it in the Lean web editor.
Dependency graph
Audit surface: 5 project declarations, 25 external constants
✓ Proved: no sorry anywhere in its closure
This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.