- formulasearchengine

General

Display information for equation id:math.220078.7 on revision:220078

* Page found: Lebesgue measure (eq math.220078.7)

Occurrences on the following pages:

Lebesgue measure Eq: math.220078.7

Hash: 5f0def9af36af5128013b1dd3c7fb06a

TeX (original user input):

\lambda^*(A) = \lambda^*(A \cap E) + \lambda^*(A \cap E^c)

TeX (checked):

\lambda ^{*}(A)=\lambda ^{*}(A\cap E)+\lambda ^{*}(A\cap E^{c})

LaTeXML (experimental; uses MathML) rendering

MathML (6.136 KB / 1021 B) :

{\displaystyle\lambda^{*}(A)=\lambda^{*}(A\cap E)+\lambda^{*}(A\cap E^{c})}

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\lambda^{*}(A)=\lambda^{*}(A\cap E)+\lambda^{*}(A\cap E^{c})}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">
      <mrow id="p1.1.m1.1.23.1" xref="p1.1.m1.1.23.1.cmml">
        <msup id="p1.1.m1.1.23.1.2" xref="p1.1.m1.1.23.1.2.cmml">
          <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">λ</mi>
          <mo id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">*</mo>
        </msup>
        <mo id="p1.1.m1.1.23.1.1" xref="p1.1.m1.1.23.1.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.23.1.3" xref="p1.1.m1.1.23.1.cmml">
          <mo stretchy="false" id="p1.1.m1.1.3" xref="p1.1.m1.1.23.1.cmml">(</mo>
          <mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">A</mi>
          <mo stretchy="false" id="p1.1.m1.1.5" xref="p1.1.m1.1.23.1.cmml">)</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
      <mrow id="p1.1.m1.1.23.2" xref="p1.1.m1.1.23.2.cmml">
        <mrow id="p1.1.m1.1.23.2.1" xref="p1.1.m1.1.23.2.1.cmml">
          <msup id="p1.1.m1.1.23.2.1.2" xref="p1.1.m1.1.23.2.1.2.cmml">
            <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">λ</mi>
            <mo id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">*</mo>
          </msup>
          <mo id="p1.1.m1.1.23.2.1.1" xref="p1.1.m1.1.23.2.1.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.23.2.1.3" xref="p1.1.m1.1.23.2.1.3.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.9" xref="p1.1.m1.1.23.2.1.3.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.23.2.1.3.2" xref="p1.1.m1.1.23.2.1.3.2.cmml">
              <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">A</mi>
              <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">∩</mo>
              <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">E</mi>
            </mrow>
            <mo stretchy="false" id="p1.1.m1.1.13" xref="p1.1.m1.1.23.2.1.3.2.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">+</mo>
        <mrow id="p1.1.m1.1.23.2.2" xref="p1.1.m1.1.23.2.2.cmml">
          <msup id="p1.1.m1.1.23.2.2.2" xref="p1.1.m1.1.23.2.2.2.cmml">
            <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">λ</mi>
            <mo id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">*</mo>
          </msup>
          <mo id="p1.1.m1.1.23.2.2.1" xref="p1.1.m1.1.23.2.2.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.23.2.2.3" xref="p1.1.m1.1.23.2.2.3.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.17" xref="p1.1.m1.1.23.2.2.3.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.23.2.2.3.2" xref="p1.1.m1.1.23.2.2.3.2.cmml">
              <mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">A</mi>
              <mo id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">∩</mo>
              <msup id="p1.1.m1.1.23.2.2.3.2.1" xref="p1.1.m1.1.23.2.2.3.2.1.cmml">
                <mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">E</mi>
                <mi id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml">c</mi>
              </msup>
            </mrow>
            <mo stretchy="false" id="p1.1.m1.1.22" xref="p1.1.m1.1.23.2.2.3.2.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">
        <eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
        <apply id="p1.1.m1.1.23.1.cmml" xref="p1.1.m1.1.23.1">
          <times id="p1.1.m1.1.23.1.1.cmml" xref="p1.1.m1.1.23.1.1"/>
          <apply id="p1.1.m1.1.23.1.2.cmml" xref="p1.1.m1.1.23.1.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.23.1.2.1.cmml" xref="p1.1.m1.1.23.1.2">superscript</csymbol>
            <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝜆</ci>
            <times id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1"/>
          </apply>
          <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">𝐴</ci>
        </apply>
        <apply id="p1.1.m1.1.23.2.cmml" xref="p1.1.m1.1.23.2">
          <plus id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14"/>
          <apply id="p1.1.m1.1.23.2.1.cmml" xref="p1.1.m1.1.23.2.1">
            <times id="p1.1.m1.1.23.2.1.1.cmml" xref="p1.1.m1.1.23.2.1.1"/>
            <apply id="p1.1.m1.1.23.2.1.2.cmml" xref="p1.1.m1.1.23.2.1.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.23.2.1.2.1.cmml" xref="p1.1.m1.1.23.2.1.2">superscript</csymbol>
              <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝜆</ci>
              <times id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1"/>
            </apply>
            <apply id="p1.1.m1.1.23.2.1.3.2.cmml" xref="p1.1.m1.1.23.2.1.3">
              <intersect id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
              <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝐴</ci>
              <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝐸</ci>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.23.2.2.cmml" xref="p1.1.m1.1.23.2.2">
            <times id="p1.1.m1.1.23.2.2.1.cmml" xref="p1.1.m1.1.23.2.2.1"/>
            <apply id="p1.1.m1.1.23.2.2.2.cmml" xref="p1.1.m1.1.23.2.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.23.2.2.2.1.cmml" xref="p1.1.m1.1.23.2.2.2">superscript</csymbol>
              <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">𝜆</ci>
              <times id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1"/>
            </apply>
            <apply id="p1.1.m1.1.23.2.2.3.2.cmml" xref="p1.1.m1.1.23.2.2.3">
              <intersect id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19"/>
              <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">𝐴</ci>
              <apply id="p1.1.m1.1.23.2.2.3.2.1.cmml" xref="p1.1.m1.1.23.2.2.3.2.1">
                <csymbol cd="ambiguous" id="p1.1.m1.1.23.2.2.3.2.1.1.cmml" xref="p1.1.m1.1.23.2.2.3.2.1">superscript</csymbol>
                <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">𝐸</ci>
                <ci id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1">𝑐</ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\lambda^{*}(A)=\lambda^{*}(A\cap E)+\lambda^{*}(A\cap E^{c})}</annotation>
  </semantics>
</math>

SVG (8.608 KB / 2.822 KB) :

SVG with PNG fallback (MathML can be enabled via browser plugin) rendering

MathML (1.462 KB / 393 B) :

\lambda ^{*}(A)=\lambda ^{*}(A\cap E)+\lambda ^{*}(A\cap E^{c})

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \lambda ^{*}(A)=\lambda ^{*}(A\cap E)+\lambda ^{*}(A\cap E^{c})}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msup>
          <mi>&#x03BB;<!-- λ --></mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mo>&#x2217;<!-- ∗ --></mo>
          </mrow>
        </msup>
        <mo stretchy="false">(</mo>
        <mi>A</mi>
        <mo stretchy="false">)</mo>
        <mo>=</mo>
        <msup>
          <mi>&#x03BB;<!-- λ --></mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mo>&#x2217;<!-- ∗ --></mo>
          </mrow>
        </msup>
        <mo stretchy="false">(</mo>
        <mi>A</mi>
        <mo>&#x2229;<!-- ∩ --></mo>
        <mi>E</mi>
        <mo stretchy="false">)</mo>
        <mo>+</mo>
        <msup>
          <mi>&#x03BB;<!-- λ --></mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mo>&#x2217;<!-- ∗ --></mo>
          </mrow>
        </msup>
        <mo stretchy="false">(</mo>
        <mi>A</mi>
        <mo>&#x2229;<!-- ∩ --></mo>
        <msup>
          <mi>E</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>c</mi>
          </mrow>
        </msup>
        <mo stretchy="false">)</mo>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \lambda ^{*}(A)=\lambda ^{*}(A\cap E)+\lambda ^{*}(A\cap E^{c})}</annotation>
  </semantics>
</math>

SVG (6.056 KB / 2.512 KB) :

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$\lambda$

$A$

$\lambda$

$A$

$E$

$\lambda$

$A$

$E$

$c$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimental; uses MathML) rendering

SVG with PNG fallback (MathML can be enabled via browser plugin) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

General

LaTeXML (experimental; uses MathML) rendering

SVG with PNG fallback (MathML can be enabled via browser plugin) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

Search