Although perhaps its focus is elsewhere, maybe you should check out

Corbae, D., Stinchcombe, M. B., & Zeman, J. (2009). An introduction to mathematical analysis for economic theory and econometrics. Princeton University Press.

The authors write

The three major innovations in this book relative to mathematics textbooks are: (i) we have gathered material from very different areas in mathematics, from lattices and convex analysis to measure theory and functional analysis, because they are useful for economists doing regression analysis, working on both static and dynamic choice problems, analyzing both strategic and competitive equilibria; (ii) we try to use concepts familiar to economists - approximation and existence of a solution - to understand analysis and measure theory; and (iii) pedagogically, we provide extensive simple examples drawn from economic theory and econometrics to provide intuition necessary for grasping difficult ideas. It is important to emphasize that while we aim to make this material as accessible as possible, we have not excluded demanding mathematical concepts used by economists and that, aside from examples assuming an undergraduate background in economics, the book is self-contained (i.e. almost any theorem used in proving a given result is itself proved).

Chapter titles:

1. Logic
   2 Set Theory
   3 The Space of Real Numbers
   4 The Metric Spaces $\mathbb R^{\ell}, \ell=1,2,...$
   5 Convex Analysis in $\mathbb R^{\ell}$
   6 Metric Spaces
   7 Measure Spaces and Probability
   8 The $L^p(\Omega, \mathcal F, P)$ and $\ell^p$ spaces, $p\in [1,\infty]$
   9 Probabilities on Metric Spaces
   10 Convex Analysis in Vector Spaces
   11 Expanded Spaces