<p>We provide a mathematically rigorous Keldysh functional integral for fermionic quantum field theories. We show convergence of a discrete-time Grassmann Gaussian integral representation in the time-continuum limit under very general hypotheses. We also prove analyticity of the effective action and explicit bounds for the truncated (connected) expectation values <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma ^\textrm{c}_{m,\bar{m}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>γ</mi> <mrow> <mi>m</mi> <mo>,</mo> <mover accent="true"> <mrow> <mi>m</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </mrow> <mtext>c</mtext> </msubsup> </math></EquationSource> </InlineEquation> of the non-equilibrium system. These bounds imply clustering with a summable decay in the thermodynamic limit, provided these properties hold at time zero, and provided that the determinant bound <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\delta _C\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>δ</mi> <mi>C</mi> </msub> </math></EquationSource> </InlineEquation> and decay constant <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha _C\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>α</mi> <mi>C</mi> </msub> </math></EquationSource> </InlineEquation> of the fermionic Keldysh covariance are bounded uniformly in the volume. We then give bounds for these constants and show that uniformity in the volume indeed holds for a general class of systems. Finally we show that in the setting of dissipative quantum systems, these bounds are not necessarily restricted to short times.</p>