Indicator Function in LaTeX

The indicator function is usually a double-struck one: \mathbb{1}_{A}(x). MathJax accepts that, but in pdfLaTeX the amssymb blackboard font has capital letters only, so use \mathds{1} from the dsfont package or \mathbbm{1} from bbm there. \mathbf{1}_{A} and \chi_{A} work everywhere.

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Indicator notation

\mathbb{1}_{A}
$1_{A}$
Double-struck 1. Works in MathJax; needs a font with blackboard digits in LaTeX.
\mathds{1}_{A}
Text mode, no math preview
Double-struck 1 from \usepackage{dsfont} (pdfLaTeX). Not available in MathJax.
\mathbbm{1}_{A}
Text mode, no math preview
Double-struck 1 from \usepackage{bbm} (pdfLaTeX). Not available in MathJax.
\mathbf{1}_{A}
$1_{A}$
Bold 1: works everywhere without packages.
\chi_{A}
$χ_{A}$
Characteristic function with chi, common in analysis.
\mathbb{1}_{\{X > 0\}}
$1_{{X > 0}}$
Indicator of an event, written as a set in the subscript.
\mathbb{I}(x \in A)
$I (x \in A)$
Double-struck capital I, used in some statistics texts.

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LaTeX

Templates

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Indicator function examples

Each result below is drawn from the LaTeX under it. Copy the code, edit it on this page, or open it in the full editor.

Definition

1_{A} (x) = {\begin{cases} 1 & x \in A \\ 0 & x \notin A \end{cases}

LaTeX

\mathbb{1}_{A}(x) = \begin{cases} 1 & x \in A \\ 0 & x \notin A \end{cases}

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Expectation of an indicator
$E [1_{A}] = P (A)$
LaTeX
```
\mathbb{E}\left[ \mathbb{1}_{A} \right] = P(A)
```
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Counting with indicators
$N = \sum_{i = 1}^{n} 1_{{X_{i} > t}}$
LaTeX
```
N = \sum_{i=1}^{n} \mathbb{1}_{\{X_i > t\}}
```
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Bold 1 alternative
$1_{A \cap B} = 1_{A} 1_{B}$
LaTeX
```
\mathbf{1}_{A \cap B} = \mathbf{1}_{A} \, \mathbf{1}_{B}
```
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Characteristic function
$χ_{[0, 1]} (x) = {\begin{cases} 1 & 0 \leq x \leq 1 \\ 0 & otherwise \end{cases}$
LaTeX
```
\chi_{[0,1]}(x) = \begin{cases} 1 & 0 \le x \le 1 \\ 0 & \text{otherwise} \end{cases}
```
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Empirical distribution function
${\hat{F}}_{n} (t) = \frac{1}{n} \sum_{i = 1}^{n} 1_{{X_{i} \leq t}}$
LaTeX
```
\hat{F}_n(t) = \frac{1}{n} \sum_{i=1}^{n} \mathbb{1}_{\{X_i \le t\}}
```
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Why \mathbb{1} fails in pdfLaTeX

With \usepackage{amssymb}, \mathbb uses a blackboard-bold font that only has the capital letters A–Z. \mathbb{1} then prints a wrong glyph or nothing useful. MathJax uses its own fonts, so the same code looks right in a browser, which is why it often works in notes but breaks in the paper.

The usual fixes in Overleaf are the dsfont package (\mathds{1}) or bbm (\mathbbm{1}). With XeLaTeX or LuaLaTeX and the unicode-math package, \mathbb{1} works directly.

LaTeX

\usepackage{dsfont}
\newcommand{\1}{\mathds{1}}
% ...
\[ \1_{A}(x) \]

Notation that works in both places

If the same formula has to render in Overleaf and on a website or in Markdown, use \mathbf{1}_{A} or \chi_{A}, which need no special font. Or define one macro per target, for example \newcommand{\ind}{\mathds{1}} in LaTeX and \ind mapped to \mathbb{1} in the MathJax configuration.

Common mistakes

amssymb’s blackboard font has no digits, so the 1 is not drawn as a double-struck one.
Instead of
```
\mathbb{1}_A  (pdfLaTeX with amssymb)
```
Write
```
\mathds{1}_A  % with \usepackage{dsfont}
```
MathJax and KaTeX do not know \mathds; they do accept \mathbb{1}.
Instead of
```
\mathds{1}_A  (in Markdown or on a web page)
```
Write
```
\mathbb{1}_A
```
A plain 1 with a subscript reads like the number one, not a function.
Instead of
```
1_{A}
```
Write
```
\mathbf{1}_{A}
```

In Overleaf, MathJax and Word

Overleaf and pdfLaTeX
pdfLaTeX needs dsfont (\mathds{1}) or bbm (\mathbbm{1}) for a double-struck one; \mathbb{1} only works with fonts that include blackboard digits, such as unicode-math under XeLaTeX or LuaLaTeX.
MathJax and KaTeX
MathJax accepts \mathbb{1}; how the 1 looks depends on the fonts available to it. KaTeX’s issue tracker has reports of \mathbb{1} not rendering as expected, so \mathbf{1} is the safe fallback on the web.
Microsoft Word
Word’s equation editor can show double-struck characters, but pasted LaTeX is not converted reliably. Write the indicator here and use Copy for Word to paste it as an editable equation.