left-continuous real function

左连续函数

Analysis, Measure & PDE · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A real function is left-continuous at a if its limit along domain points increasing to a equals f(a).

实函数在 a 处的左极限等于 f(a)，则称其在该点左连续。

Example

1(0,∞)\mathbf1_{(0,\infty)} is left-continuous at 00.

Usage and distinctions

At an interval endpoint only the side belonging to the domain is tested.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Michael Taylor — Introduction to Analysis in One Variable§3.1, relative-domain continuity · Checked 2026-10-14
  2. OpenStax — Calculus Volume 1§2.4, Continuity from the Right and from the Left, left-continuity definition · Checked 2026-10-15

Translation sources

  1. 中国矿业大学数学学院 — 数学分析讲义，第四章§1 一、函数在一点的连续性, 定义2 · Checked 2026-10-14
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