A note on measurable modifications

We present, with purely didactic aims, a simple and essentially self-contained proof of two necessary and sufficient conditions for existence of a measurable modification of a stochastic process with values in a separable complete metric space.Existence of a measurable modification of a stochastic process continuous in probability is an immediate consequence.

Authors

Publication Details

Journal
Kybernetika
Published
2026-01-13
DOI
https://doi.org/10.14736/kyb-2026-1-0007
Primary Topic
Holomorphic and Operator Theory
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

A note on measurable modifications

Martin Ondreját, Jan Seidler
Kybernetika
Holomorphic and Operator Theory
article

A note on measurable modifications

Martin Ondreját, Jan Seidler
article en

Abstract

We present, with purely didactic aims, a simple and essentially self-contained proof of two necessary and sufficient conditions for existence of a measurable modification of a stochastic process with values in a separable complete metric space.Existence of a measurable modification of a stochastic process continuous in probability is an immediate consequence.

Kybernetika
Zero hunger
Openalex Percentile: Top 88%
Holomorphic and Operator Theory
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

A note on measurable modifications — Martin Ondreját, Jan Seidler · Kybernetika (2026) | TGRS Research Map | TGRS