Beschreibung:
<jats:title>Abstract</jats:title>
<jats:p>We investigate the possibilities of integration on the minimal <jats:inline-formula>
<jats:tex-math><?CDATA $\mathbb{Z}_2^2$?></jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="double-struck">Z</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aad076eieqn2.gif" xlink:type="simple" />
</jats:inline-formula>-superspace. Two definitions are taken from the works by Poncin and Schouten and we examine their generalizations. It is shown that these definitions impose some restrictions on the integrable functions. We then introduce a new definition of integral, which is inspired by our previous work, and show that the definition does not impose restrictions on the integrable functions. An interesting feature of this definition is the emergence of a spatial coordinate which means that the integral is defined on <jats:inline-formula>
<jats:tex-math><?CDATA $\mathbb{R}^2$?></jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aad076eieqn3.gif" xlink:type="simple" />
</jats:inline-formula> despite the fact that the <jats:inline-formula>
<jats:tex-math><?CDATA $(0,0)$?></jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
<mml:mo stretchy="false">(</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo stretchy="false">)</mml:mo>
</mml:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aad076eieqn4.gif" xlink:type="simple" />
</jats:inline-formula> part of the minimal <jats:inline-formula>
<jats:tex-math><?CDATA $\mathbb{Z}_2^2$?></jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="double-struck">Z</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aad076eieqn5.gif" xlink:type="simple" />
</jats:inline-formula>-superspace is <jats:inline-formula>
<jats:tex-math><?CDATA $\mathbb{R}.$?></jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aad076eieqn6.gif" xlink:type="simple" />
</jats:inline-formula>
</jats:p>