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Construction junctions are diamonds. They show where multiple structures must coexist on the same carrier and satisfy compatibility conditions.

Canonical static concept record

Filtered probability space

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Summary

A probability space equipped with a filtration of sub- $\sigma$ -algebras.

Record metadata

Canonical name: Filtered probability space
Concept ID: filtered_probability_space
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Probability
Domains: Probability, Measure
Alternate terminology: No alternate terminology is currently authored for this record.

Carrier(s)

probability space $(\Omega,\mathcal F,\mathbb P)$

Data

filtration $(\mathcal F_t)_{t\in T}$

Axioms / constraints

$\mathcal F_t\subseteq\mathcal F$ for every $t\in T$

Concept sources

Wikipedia — Filtered probability space — Filtered probability space · expository · source ID wp-filtered-probability
nLab — Filtered probability space — Filtered probability space · mathematical reference · source ID nlab-filtered-probability-space
Durrett — Probability: Theory and Examples — Probability: Theory and Examples · textbook · source ID durrett-probability

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

probability + filtration(construction junction)Filtered probability space

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: j_filtered_probability__out
Relation type: Combine compatible structures combine-compatible
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: impose compatibility

Authored explanation

Use a filtration of sub- $\sigma$ -algebras of the probability space.

How to interpret this relation type

Feed several structures into a construction junction and impose compatibility between them.

Relation sources

Wikipedia — Filtered probability space — Filtered probability space · expository · source ID wp-filtered-probability
Durrett — Probability: Theory and Examples — Probability: Theory and Examples · textbook · source ID durrett-probability

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.